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Yes the relays are the most common problem for the vacuum headlights. Generally though you have better vacuum at low RPMs, so it's puzzling why it works when you rev. Maybe you have both low vacuum and a bad check valve. That might explain why they operate when the engine is revved. Lack of vacuum with a bad check valve will usually raise and lower the headlights when the engine is first started.
Not uncommon with a lot of HP. Wild camshaft will cause that problem. If you can live with the condition, leave it alone. The wiper door may also be affected. But not on yours if the door is not used any more....