Yes, the pilots usually waited out the storm in the plane, fortunately the monsoon storms were usually short-lived, about a half hour max. So the pilot would either wait at the EOR marshall area, with the engines (and cockpit A/C

) running, or go directly back to the flightline parking spot and shut down and get out quickly.
On rare occassions, if the plane(s) had enough fuel, they would hold in the air and fly around 'till the storm passed.
After I got certified for the APU (Auxillary Power Unit, a small turbine engine in the rear of the aircraft which provides power, hydraulic pressure and bleed air for engine starting) operation, I discovered a few neat things to do while waiting out the rain.

For example, the aircraft's radio can tune in some of the VHF local T.V. channels. It was quite surreal to be sitting in a military fighter, on a dark flightline, while listening to Johnny Carson.

Another fun thing to do was open the speed brakes (on the A-10, about the size of a sheet of plywood) and waggle the stick, thus whacking the poor unsuspecting fool standing under the wings.
