Nine times out of ten , poor electrical performance on Morgans is down to a bad earth, but both bulbs share a common earth so this is unlikely to be the cause.
There is no relay on the headlight circuits , but fitting one is really good idea, it protects the circuit and gives much better voltage at the bulb. I think there is a fitting and circuit guide on here somewhere.
If Richards ideas don't bear fruit (or light?) come back here and we will try to come up with other ideas.