Could be the transmission selector pad. The membrane behind the D-N-R buttons get stiff as they age and the contact points behind on the circuit board no longer make good contact. If the keypad is cold it would make them even stiffer. Seems to make sense since it eventually starts working after the keypad has been on for a few minutes as they do generate a bit of their own heat - perhaps enough to soften up the membrane behind the buttons. I honestly feel that if it were a fluid viscosity, flow or fluid level issue that it wouldn't want to select any gear, not just neutral.
Changing your trans fluid and filters is never a bad idea, however I suspect that has nothing to do with your problem you've posted. Along with the buttons not working properly, such as having to push on them real hard or complete failure, many have had problems with the power supply going bad in these older WTEC-II shifter controllers starting at about 15 yrs of age (including me). Might I suggest calling John at Transmission Instruments
about taking a look at your keypad. For $300.00 he can rebuild your WTEC-II controller completely - replace the power supply and replace the shift buttons and membrane. When/if the power supply fails you're not going anywhere until it's replaced, I know from 1st hand experience! Allison wants over $2000.00 to upgrade to a newer WTEC controller and Trans control module, John charges around $300.00 to rebuild your controller which is EASY to remove, approximately 15 minutes. Visit his website, lots of pictures, including this one of the VERY common Neutral button wearing out, which is very obvious.