1991 mustang lx 5.0 liter gear shift problem

Start by checking for vacuum leaks, compression then a scan for fault codes. One of those should turn up a problem

1991 GEO STORM 1.6L 4-cyl Engine Code 5 DOHCCAPACITIES
Engine, with filter.......... 3.2 quarts
Cooling System, W/ MT Initial Fill.......... 7.4 quarts
Cooling System, W/ AT Initial Fill.......... 8.0 quarts
Automatic Transmission, Initial Fill........ 4.3 quarts [1]
Automatic Transmission, Total Fill......... 7.0 quarts
Manual Transmission, ..........4.0 pints[1] With ENG at operating temperature, shift through all gears.
Check fluid level in PARK and add fluid as needed.1991 GEO STORM 1.6L 4-cyl Engine Code 6 SOHC
1992 GEO STORM 1.8L 4-cyl Engine Code 8 DOHCCAPACITIES
Engine, with filter.......... 4.0 quarts
Cooling System, W/ AT Initial Fill.......... 8.0 quarts
Cooling System, W MT Initial Fill........... 7.4 quarts
Automatic Transmission, Initial Fill........ 4.3 quarts [1]
Automatic Transmission, Total Fill......... 7.0 quarts
Manual Transmission, .......... 4.0 pints[1] With ENG at operating temperature, shift through all gears.
Check fluid level in PARK and add fluid as needed.

http://www.autozone.com/autozone/repairinfo/repairguide/repairGuideContent.jsp?fromSearchPage=true&pageId=0900c15280251027&partName=Neutral+Safety+and+Back-up+Light+Switches&partId=0900c15280251027 Here you go,try this.

fuel pump relay is located under the drivers seat.

No, those sensors are seperate from transmission, should be a solenoid that is electrically controlled inside the transmission that controls the shifting.

you may have a broken selector fork or sencronising ring assemble,

It's a short dipstick, located at the front of the engine compartment, very low, towards the bottom of the radiator.

Hah.. time for a new car, hey?

what happens if you pull the shift lever into gear to cut off the neutral-park safety switch? This cuts pwer from the key to the starter solenoid. If that fixes it, replace the igniton switch.

check all of the vaccum lines and the one behind the throttle body and the EGR valve and the vaccum pump.