All the obd1 cars ive dealt with have never had an issue being on or off. Voltage signal was identical either way. The ecu is gonna put out a max of 5 volts to the tps whether your battery volts is 12 or 14. Low battery voltage could possibly cause a problem but even then the ecu is set to output 5 volts. Which is why I asked him to check and make sure he has 5 volts to the tps. Unplug it to isolate it and check for 5v. Also check your ground to it as well by using the tps ground as the ground for your multimeter and then a good known ground such as on the battery post itself and see if you get different readings.