The very first place(s) to start with issues on 240 lights:

Open up all the connectors (the bullet ones usually go first - and often do funny stuff), unplug all the sockets, undo all the ground screws -spray with PB-Blaster and abrade with brass brush and other implements as necessary. Soak with PB Blaster for a few hours/little while (as required), clean with contact cleaner and button it back up.

Yours does sound like a ground issue...but I have seen HB Relays go south...don't forget to clean the relay socket and blades on the relay.
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