There are different relays with different functions that all look the same at first glance. As Byron said, you want an 87b relay (the ID marking on the centre terminal). Take a close look at the relay the auto parts store sold you - it probably has an 87 identifier for the centre pin. This means that it and the other output pin (another 87) are always joined together. The 87b pin is joined to the 87 only when the relay switches on.

The remaining - and much more common - simple cube relay has an 87a centre terminal. This is a double throw relay (usually shown as SPDT in parts catalogues). The 87a pin is connected to the input 30 pin when the relay is not activated. When you trigger the relay the 87a is disconnected, and the 87 connects to the 30.

So if they give you the wrong relay, weird things will occur. The correct relay is a black Bosch with a "K" on top in Green paint (as Byron stated), but any relay that can handle 15Amps and has the centre 87b pin will do.

That said - a bad headlight switch sounds like the real problem. A self-serve junkyard should have one for a couple of $$.
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Bob (son's 81-244GL B21F/M46, dtr's 83-244DL B23F/M46, my 94-944 B230FD and 89 745 (LT-1 V8); hobbycar 77 MGB, and a few old motorcycles)