You could remove the cap, zip tie the kill switch parts and see if it runs before drilling the cap but a small hole won't hurt any.
I was thinking try running it on the lawn without the cap but drilling a new small hole won't kill as much grass.
At 12 years, if it sat outside much you would not be wasting a bunch of money replacing fuel lines from the tank. I would think you could clean the filters with brake cleaner or carburetor cleaner if you drain the tank and replace the fuel lines.
1992 Tbird LX 5.0, 3.73 gears, 1995 Cobra intake, deleted air silencer, 2.5" mandrel bent dual exhaust, SCP shorty headers. Updated four-hole fuel injectors. SK shift kit in AOD. Vogtland 0.9" springs, Tokico and Bilstein shocks.