Investment in cheap digital voltmeter (multimeter) better value IMO than the 2 wire automotive tester light, since you get actual volts and can use it to measure resistance. I recently bought one for under $10 US to replace my 25 yr old Radio Shack analogue multimeter (neighbor borrowed and made fatal error (for meter) after checking fuses, of measuring house volts with meter still set for ohms, poof).
Suggest you examine hi-speed fan circuit first since that can be commanded on by turning on a/c.
Engine on, have someone turn on a/c while touching the hi-speed relay to see if it's coil energizes.
If ok then with ignition off pull relay.
Engine on, a/c on, measure volts to ground on relay socket terminal 3.
If volts ok then ignition off, insert relay and separate 2 wire connector at top of fan shroud.
Engine on, a/c on, measure volts on GN/BL wire-from-fuse-panel's pin.
That should get you started.