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@gbj_tester
Possibly CBX750F? IIRC, the combination of a 16" front wheel and none too stiff frame (thin steel tubes, didn't use the engine as a stressed member) would lead to a wobble which didn't actually develop into a tankslapper if you sat up and took your hands off at low speed, i.e. <30mph. There was a resistance by manufacturers in those days to fitting steering dampers on stock bikes, as it looked like an admission that they had got the handling wrong. Suzuki stopped the pretence with the GSXR-11, and now steering dampers are pretty much standard issue on sports bikes.
On the OP's problem, does it wobble when you freewheel or only when pedalling? (Obviously, if it's fixed at the moment you'd need to fit a freewheel to test this)