Ok I really hope it is your relay.
Getting the unit repaired by a qualified technician will cost anywhere from $95 to $200 and buying a used unit costs around $150 and up. (Those numbers reflect what I have found but I’m sure others have found better deals)
I find it rare for electrical parts to go bad without some type of abusive heat where the relay is mechanical meaning it has moving parts and of course the contacts in the relay can get dirty, pitted, or just not get good contact. So lets test it.
Note: I am no professional nor am I trained for this. I'm just a 24 year old guy who likes to tear things apart and rebuild them to test and improve my skills but I find my research skills allow me to make any qualifying piece of paper unnecessary.
2nd Note: if your ABS looks to be the same as mine then you can skip down to the relay testing part and skip the disassembly. You really only need to disassemble the unit if the relay tests bad but I had to disassemble it to get the part number off the relay to lookup the datasheet.
It took me about 45min to desolder and take apart the ABS unit. It is difficult and in the pictures you can see why.
So here are the tools I used. I had a 40watt soldering iron and I strongly recommend a smaller tip than the one I used also I used a bulb vacuum desoldering tool (that red thing) to suck the solder off the board. This bulb had a large tip which made it hard to get into the small spaces. I would recommend a different one with a smaller tip to get into the tight spaces.
Taking off the board is a challenge. You have to take off all the extra solder on all the spots where one of the connectors connects to the board and where the solenoids connect to the board. I had to unsolder the solenoids because the were blocked off.
The case was blocking them.
Then you apply a little upward pressure, I used a screw driver, then you just move around heating up the connections one by one slowly allowing the board to separate from the plastic case. Sounds hard but fairly easy with patience (it's a slow process).
This was the hardest spot.
So I got a little rough and had a small mishap but all is good I just glued it back down and when I reassemble it will be just fine. So take you time.
This is everything separated.
So here is what we were looking for, the relay.
So I typed "JSM1-12v-5-H38 datasheet" into google and found the datasheet.
This is an automotive 12v high capacity 15A relay with a 6.3 volt pick-up meaning you need at least 6.3 volts to actuate it. (I used a 9 volt battery)
This is what the datasheet revealed.
I don't know how familiar you are with relays but from the datasheet you should be able to figure out how to test it. Just test for continuity from the com to the no voltage side and then apply 9v to the coils and test for continuity from the com to the voltage side. This picture is me testing the no voltage side with my multimeter. I didn't have enough jumpers to take a pic of me testing the power side with voltage applied but mine tested good.