*Need help on how to wire up a switch panel*

It SOUNDS like you are fine. The orginal bypass brown, went directly from the ignition switch, through the bulkhead, to the COIL side of the ballast. In other words, the brown bypass went (electrically) to the coil+ So if you hooked a wire from the newer start relay pictured to the coil+ you should be good.

You can confirm that by taking the brown off the start relay, cranking the engine, and checking that the terminal marked "BAL" is hot during cranking. Once again, you'll have to check that with the wire disconnected, otherwise, you'll get a feedback situation.