Hi There
I would try reflowing the 3 signal inputs using some liquid flux.
I also notice that you are using a megadrive cable. These cables have inline components and its recomended you remove the three resistors on the tmsrgb board and jumper them instead. If your cable also has a csync inline resistor you will need to connect to the other csync pad on the tmsrgb.
If you have carried out the above and confirmed continuity on the RGB lines from the tmsrgb output pads to the scart plug pins then its possible the tmsrgb board is not functioning correctly