Unfortunately could be few things so mention this to those idiot mechanics of yours.
1) It sounds like the FUEL PUMP is quiting for some reason. Now the pump could be wearing out because it is an older car but maybe not (so don't go out an by one!).
2)) : check the fuel gauge - if it drops, it could be the FUEL PUMP RELAY dropping out.
3) That fuel pump is also powered by an OIL PRESSURE SWITCH that as long as there is oil pressure in the engine keeps that pump running. Assuming the relay drops out and itis running gon the oil switch, coming to a stop sign could drop the oil pressure en ought that the oil switch opens, although it is supposed to oper ate on something like 3PSI. That's another scenario.
4) loosed the gas cap and leave it loose to see if the tank is forming a vacuum thus not allowing the fuel out - VACUUM LEAK
5) Check WIRES there is a connector on the fuel tanks and out of that connector comes a ground wire that bolts to the body somewhere. it is the bround for both eh pump and the fueled sender and must be clean and tight.
So it coould be a power or pump problem or loose connect.
LMF Canada
Perhaps a vacuum leak
On my 1993 Oldsmobile 88, it is number "8"
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The 1994 Oldsmobile Cutlass turn signal relay switch can be found below the dashboard. The relay switch will be on the drivers side of the passenger compartment.
Try checking the fuel injectors
If you have the 2.3 engine, one possibility is sludge in the Throttle Body.
Stall the car to stop the engine.
Maybe next time just turn it on.
check brake fluid level.
Try checking and /or replacing the IOC valve - that is the Idle Air Control valve.
if only the turn signals are not working,you should replace the flasher can
it sounds like a bad flasher which is directly behind the switch/button that is used to turn four ways on