The term “Nirira namastaka” is found in all editions of The Mahatma Letters to A. P. Sinnett (1st, 2nd, and 3rd editions, p. 44, letter #9; chronological edition, p. 62, letter #18). The context may be seen in the following quotation (quoted from the 3rd edition):
“When our great Buddha—the patron of all the adepts, the reformer and the codifier of the occult system, reached first Nirvana on earth, he became a Planetary Spirit; i.e.—his spirit could at one and the same time rove the interstellar spaces in full consciousness, and continue at will on Earth in his original and individual body. For the divine Self had so completely disfranchised itself from matter that it could create at will an inner substitute for itself, and leaving it in the human form for days, weeks, sometimes years, affect in no wise by the change either the vital principle or the physical mind of its body. By the way, that is the highest form of adeptship man can hope for on our planet. But it is as rare as the Buddhas themselves, the last Khobilgan who reached it being Tsong-ka-pa of Kokonor (XIV Century), the reformer of esoteric as well as of vulgar Lamaism. Many are those who ‘break through the egg-shell,’ few who, once out, are able to exercise their Nirira namastaka fully, when completely out of the body. Conscious life in Spirit is as difficult for some natures as swimming is for some bodies.”
It appears to be an important technical term, pertaining to advanced Buddhist metaphysics. However, no such term could be identified in the 93 years since the Mahatma letters were published, even with the availability in recent decades of large numbers of primary Buddhist texts. Since photographic images of the Mahatma letters have become available, it has become possible to see if there is another way to read this term in the handwriting of the letter (http://theosophy.wiki/ML/18-12_6117.jpg). Daniel Caldwell did this last year (April, 2016), and saw that it could be read as “Nirvva namastaka.” If we now break the word differently, we find the familiar Buddhist term, “nirvvana”; i.e., “nirvana” (nirvāṇa). Daniel could then search the internet for “nirvvanamastaka.” Sure enough, as Daniel informed me, it turned up in the entry on “Buddhism and Buddha” in The New American Cyclopaedia, vol. 4, 1869 and 1870, p. 66.
Just as the similarly long unidentified phrase “Kam mi ts’har” found in the Mahatma letters was copied directly from a book existing at that time, as shown by Antonios Goyios (http://www.blavatskyarchives.com/kammitshar/kammitshar.htm), so with this term. It is even found hyphenated at the end of a line in The New American Cyclopaedia at exactly where it was wrongly broken in the Mahatma letter: Nirvvā-namastaka. There can be no doubt that this is the source from which it was taken by the Mahatma or his chela amanuensis. As Daniel pointed out, the Mahatma letter also has: “Many are those who ‘break through the egg-shell,’ few who, once out, are able to exercise their Nirira namastaka fully, when completely out of the body.” The New American Cyclopaedia has (p. 66): “He who breaks its fetters, ‘breaks through the eggshell’ and escapes the alternation of births.” Later on in this Mahatma letter we also read: “Matter found entirely divorced from spirit is thrown over into the still lower worlds—into the sixth ‘Gati’ or ‘way of rebirth’ of the vegetable and mineral worlds, and of the primitive animal forms.” (3rd edition, p. 47; the 1st and 2nd editions wrongly have ‘Gate’ for ‘Gati’). The New American Cyclopaedia has (p. 66): “In some cases the soul of man may sink even below the 6 Gatis or ways of rebirth into the vegetable and mineral way; . . .” Of course, the Mahatma letter used this term and these phrases somewhat differently, but clearly adopted them from this source.
About nirvvānamastaka, i.e., nirvāṇa-mastaka, The New American Cyclopaedia has (p. 66):
“The final goal of Buddhistic salvation is the uprooting of sin, by exhausting existence, by impeding its continuance; in short, by passing out of the Sansāra into the Nirvāna. The signification of the latter term is a prolific subject of discussion and speculation with the different philosophic schools and religious sects of Buddhistic Asia. Its interpreters prefer vague definitions, from fear of offending sectarians. It means the highest enfranchisement; to theists, the absorption of individual life in God; to atheists in naught. The Thibetans translate it by Mya-ngan-los-hdah-ba, the condition of one freed from pain; eternal salvation, or freedom from transmigration. Its etyma are: nir, not; van, to blow, and arrow; its orthography is Nirvvāna; its collaterals are: Nirvvānamastaka, liberation ; nirvvāpa, putting out, as a fire, &c. It is Nibbāna in Pali, Niban in Burmese, Niruphan in Siamese, Ni-pan in Chinese.”
So is nirvāṇa-mastaka, then, an important technical term pertaining to advanced Buddhist metaphysics? No. It is a ghost word, a word that appeared in a dictionary and was copied in other dictionaries, but has not been found in use in Sanskrit texts. According to my research, it first appeared in the 1832 second edition of Horace Hayman Wilson’s Sanskrit-English dictionary (A Dictionary in Sanscrit and English, Calcutta). It is there written nirvvāṇamastaka, and defined as “liberation,” with the etymology nirvvāṇa and mastaka, “head, chief” (p. 477). It was obviously copied from there by the unnamed writer of the “Buddhism and Buddha” entry in The New American Cyclopaedia. It is not found in the 1819 first edition of Wilson’s Sanskrit-English dictionary, nor is it found in the 1900 revised edition of Wilson’s dictionary. We may guess that one of Wilson’s assistants may have found it in some Sanskrit kośa, lexicons that often list words that are not found in use, and put it in the second edition of his dictionary. From there it was copied (but without doubling the “v”) in the relevant 1865 volume 4 of the massive 7-volume Petersburg Sanskrit-German dictionary (Sanskrit-Wörterbuch, by Otto Böhtlingk and Rudolph Roth, St. Petersburg), where it is followed by “!” and specifically stated as coming from Wilson (p. 209). It was retained in the relevant 1882 volume 3 of the shorter 7-volume Petersburg dictionary (Sanskrit-Wörterbuch in Kürzerer Fassung), keeping the “(!)” after it (p. 219). It was likewise copied in Monier Monier-Williams’ Sanskrit-English Dictionary, both his 1872 first edition and his 1899 enlarged edition, where it is also specifically stated as coming from Wilson. It is also found in Vaman Shivram Apte’s Sanskrit-English dictionary, but no source is given. This typically means that Apte did not find it in any Sanskrit text, but copied it from previous dictionaries. It is even found in the Vācaspatyam Sanskrit-Sanskrit dictionary, where it is defined like a compound of such type would have to be construed: nirvāṇam nirvṛtir mastakam iva yatra, i.e., as nirvāṇa that is like the head. It is not, however, found in the earlier Śabda-kalpa-druma Sanskrit-Sanskrit dictionary. Nor is it found in Franklin Edgerton’s Buddhist Hybrid Sanskrit Dictionary. My electronic searches of massive quantities of Sanskrit texts, now possible, have failed to yield a single occurrence of this term. I even posted a query for a “textual source for nirvāṇa-mastaka” to the Indology e-list on Jan 13, 2017, consisting of several hundred Indologists working today. No one was able to come up with a textual source for this term.
The Mahatma letter is describing a form of adeptship that is not described in any Buddhist text known to me; yet in doing this the Mahatma or his chela amanuensis used a ghost word copied from an 1869 book that was in turn copied from an 1832 dictionary. We have seen other cases of this type of copying from then existing books in the Mahatma letters, as found by Antonios Goyios in the article linked above (“Tracing the Source of Tibetan Phrases Found in Mahatma Letters #54 and #92”), and there are still others that could be cited. The relevance of this to students of Theosophy is that, due to the methods used by the Mahatmas in writing their letters, terms such as this found in the Mahatma letters may not be actual Buddhist technical terms that can be found in the Sanskrit texts. As we know from a number of statements made by the Mahatmas in their letters, their method of writing was to surround themselves with material on the topic at hand that is impressed upon the ākāśa, and to draw from it what they needed. They were not native English speakers. Their letters constitute personal correspondence, often written in haste, not articles written for publication. The Buddhist terms and quotations found in the Mahatma letters almost always come from then existing books, and therefore cannot be relied upon for accuracy.