It possible an mot garage might change a sidelight bulb immediately as a goodwill gesture, at minimal cost, or even free of charge if you carry a spare bulb , but only if its a really quick and easy. Its increasingly common that front bulbs, especially headlight bulbs , need some dismantling to access .
I think the mk 1 side light can be accessed by partly unclipping the inner wheel arch liner . Technically not difficult but one or more plastic trim fixing plugs may break and need to be replaced.Not a problem if you have correct type of replacement clips available. And the knowledge of exactly how to do it on a comparatively uncommon car. I'm not surprised they were reluctant.