Turn signal

When you say signal relay, are you referring to the flasher? Was it replaced or just checked? If the light comes on but does not blink (as you described) then the flasher is not working

Here is the testing procedure

Inspect the relay and fuse/relay box socket terminals to be sure they are all making good contact.
If the terminals are bent, loose, or corroded, repair them as necessary, and recheck the system.
If the terminals look OK, Go to step 4.
Do the following input tests:
If any test indicates a problem, find and correct the cause, then recheck the system.
If all the input tests prove OK, the turn signal/hazard relay must be faulty; replace it.

CAVITY TEST CONDITION REFERENCE CHART

Cavity Test condition Test: Desired result Possible cause if desired result is not obtained
6 Under all conditions Measure the voltage to ground: There should be battery voltage.
Blown No. 16(15 A) fuse in the under-hood fuse/relay box
Faulty under-dash fuse/relay box
An open or high resistance in the wire
1 In all ignition switch positions Check for continuity to ground: There should be less than 0.2 V.
Poor ground (G501)
Faulty under-dash fuse/relay box
An open or high resistance in the wire
2 Connect terminal No. 6 to terminal No. 2 with a jumper wire. Check the turn signal lights operation: The left turn signal lights and indicator should come on.
Blown bulb
Poor ground (G601, G301) or an open in the ground wire
An open or high resistance in the wire
3 Connect terminal No. 6 to terminal No. 3 with a jumper wire. Check the turn signal lights operation: The right turn signal lights and indicator should come on.
Blown bulb
Poor ground(G201, G602) or an open in the ground wire
An open or high resistance in the wire
4 Ignition switch ON (II) and turn signal switch in Left position. Measure the voltage to ground: There should be about 10 V.
Poor ground (G501) or an open in the ground wire
Faulty turn signal switch
Faulty under-dash fuse/relay box
An open or high resistance in the wire
Faulty combination switch control unit
(1)
Faulty MICU
(1)
5 Ignition switch ON (II) and turn signal switch in Right position. Measure the voltage to ground: There should be about 10 V.
4 Hazard warning switch ON Measure the voltage to ground: There should be about 10 V.
Poor ground (G501) or an open in the ground wire
Blown No. 16 (15 A) fuse in the under-hood fuse/relay box
Faulty under-dash fuse/relay box
Faulty hazard warning switch
An open in the wire
Faulty MICU

Let me know how it goes

Best, Ken

Please follow the power lead of the trailer brake to see where it plugs in, this could be the problem. I think the back up lights could be the ground so please double check it.