Vapors of Aqueous solutions
You may want to read the Wikipedia article on TMAH.  While it does decompose, it may not produce the methanol you are expecting.  Also, heat is also involved in this process, so you may need to heat and, in the process, vaporize much of the water to get this decomposition to go.

TMAH, in common with many other TMA salts containing simple anions, decomposes on heating into trimethylamine.[1] Dimethyl ether is a major decomposition product rather than methanol.[2] The idealized equation is:


$\ce{2 NMe4+OH− → 2 NMe3 + MeOMe + H2O}$

Such a rearrangement suggests an irreversible reaction.  The Wikipedia article also indicates that TMAH is not obtained by combining trimethylamine with methanol anyway.  Instead, a metathesis between a tetramethylammonium salt such as the chloride and an alkali hydroxide is used.
Cited References:
1.
Lawson, A. T.; Collie, N., &quot;The action of heat on the salts of tetramethylammonium&quot;. J. Chem. Soc., Trans., 1888,53, 624-636. doi:10.1039/CT8885300624.
2.
Musker, W. Kenneth. (1964). &quot;A Reinvestigation of the Pyrolysis of Tetramethylammonium Hydroxide&quot;. Journal of the American Chemical Society. 86 (5): 960–961. doi:10.1021/ja01059a070.