Yes it could.
Is your headlight switch and blinker switch the same? If so, this is called the combination switch. Sounds like it is bad and needs to be replaced. Not uncommon for these to break.
there are several problems that could cause this on a jeep one is the ignition switch, the starter, the gear changer on the transmission.
Probably cause by a worn out/defective brake light switch.
pressure switch
ignition switch i promise
Bad switch or transmission not completely in park. Try putting a little pressure on the gearshift.
Possibly the pressure cycling switch.
corroded seal in caliper - leaking break fluid. if you dot3 break fluid, you ruined the seals, the jag needs dot4 or dot 5.
It is decently possible that it is an electrical short making it register the mist setting instead. A test of this would be to turn it to the mist setting to see if it turns off, as shorts can cause triggers to switch.
A bad fuel pump can cause stalling. The oil pressure will show low oil on the lights or gauges but if the pressure is ok then the switch should not cause stalling.
It could cause a high reading on the gauge.
No it will not.