Turn Signal Relay Issue

Good morning,
I am trying to sort out an issue with my turn signal relay. I bought both the normal mechanical and the Heavy Duty one (Electric and for LED). I have both incandescent and LED 1157 bulbs to swap between.

If I connect the pink multi-wire V shaped connector to the relay, and use the stalk, I see the green light appear in the dash, but it is solid and so is the light outside.

However, if I take my test light, that is of course clipped to ground, and I touch the tip to the prong on the relay (I believe the X not the L .. I think is for Load to wire), I can feel the relay click like it is working. But, as soon as I remove the test light probe it stops. In my bird brain thinking, I said, "Ah-ha! it just needs to be grounded". Since the test light connects to ground. But, when I took a pigtail from the door sill and touched the relay, it sparked!

So, I am confused....

I also cannot get my brake lights to work. I think that is a bad Stop Light Switch. I get hot on both terminals of the brake switch and I am thinking that is wrong. But, as you can see, I am no electrician.