This is not a valid test.
The M119 LH-SFI NSS has two completely separate functions. One is for the starter lockout and reverse lights. The other, using a separate set of pins, is a gear position indicators. Your mechanic tested the first function and its good. But he did not test the second function. This requires SDS with HHT-Win to view live data from the E-GAS module in each gear position. See post #4 above. Normally this will store a fault code on the E-GAS module as well, but it may be possible to have the problem without a stored code.
See above for the full test, checking both gear position in live data AND also the engine RPM because the tach may not be accurate either. ALSO, the NSS must be adjusted properly. A good NSS wont work right if not adjusted per FSM procedure.
Did you install the new NSS yet?
UH-oh. Those are NLA, but you can probably locate a good used one.