If you want to do some electrical work you could install a transfer case Neutral switch for the electric shift motor
Shift motor seen here:
https://www.explorerforum.com/forums/index.php?threads/how-to-rebuild-4x4-shift-motor.123542/
In the 4th picture you can see the transfer case shift rod in 2WD position
Just opposite it is Neutral position, unmarked
In the 5th and 6th pictures you can see the Contact Wheel and contacts
As the 4x4 control module powers the motor the contact wheel moves with shift rod position, Contacts have a 2WD, 4high, Neutral, and 4low setting
This is why there is a delay from when you select 4high and the dash light comes on, the contact wheel must move to 4high position before 4high light comes on.
Neutral is just not included in the selections on the dash switches
Ford used to sell add on Neutral switch for flat towing, but not any more
You could build one with a toggle switch, two relays and an LED light to show when Neutral was set on contact wheel
Yes, towing with manual transmission in Neutral means the counter shaft is not turning, so output shaft is not being lubed very well
In normal driving the input shaft is turning, powered by the engine, which turns the lower counter shaft which pulls oil/ATF up from bottom of trans to the top keeping upper part wet with oil/ATF
This doesn't happen if only the output shaft is turning.
When you stop, start up the engine, you can leave it in Neutral, but let clutch pedal up, let it run for a minute or two, that will get oil/ATF to the top
Transfer case in Neutral doesn't have that issue