If there is a relay I'm pretty sure it would be used for both high beams.
Yep, so if there are separate fuses then I'd guess that's where the feed splits left and right, just before the fuses. On my much older (1986) car there's only one fuse and the feed splits immediately afterwards on the downstream exit from the fusebox.
I'm pretty sure it's going to be a corroded connector somewhere, and my favourite place to look would be where the wiring is exposed the most to road dirt and water ingress.
My fuses are up on the top of the bulkhead under the bonnet and are reasonably well protected, so if it were my car I'd start by looking under the wing in the region of the front suspension as it's pretty exposed to spray there. Then I'd pull the headlamp bowl out of the wing and having a look in there as it's likely to not have been disturbed and might have been leaking for a long time.
If OTOH your fusebox and relays are up under the dash I'd start there, as Morgans are prone to having water leaks under the scuttle and you can get a fair bit of corrosion if the car has been driven regularly in poor weather.
