Based on the fact that you said the relay clicks when you push on the connector, I would say you still have a bad solder joint... even if it looks good. Resolder it good and then see how things work..

If you were getting the P0335 code, that would be the CPS acting up.... You also didnt mention trouble with it cranking and not starting.. another indication of CPS bad...

The relay control module sounds like your issue..... but it is an easy and free fix(if you can do it)..