Turn Signal Relay Issue

2. All the lights in all 4 corners light up. They just do not flash.

First thing I'd do is access one or two lamps that are easy to get to. Clip your test lamp to a good ground, like the trunk floor latch, and probe the metal socket shell. You should NOT get a light. If you do, it shows the shell is ungrounded. HOW can they light in that case? The TS bulbs and power go in series through the park/ tail filaments and to ground

If the shells are grounded, I'm not sure of an answer. Is the flasher a direct 2 pin plug in replacement? Any chance it could be wired backwards that is power going to the lamp terminal?

Is this a special flasher you've bought and if so, post a link and or any documentation with it?

Flashers "used to be" simple. They needed a couple of lamps for a load, and they were wired in series with the load. They were a thermal activated device. The current from the load of the lamps heated up a little unit in the flasher, and heated a bi-metal strip. Same as used in home heating thermostats. They bend when they heat up due to the different expansion rates of the two metals used. So they bend, and break contact, and cool off and remake contact........and all over again