Shaking at idle while in gear is pretty common on those. The fix is a rack damper adjustment or possibly replacement (no big deal) and/or motor mounts. Parts are not expensive but parts+labor if you pay someone else to do it could run a few hundred.

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Whoever said there's nothing more expensive than a cheap Mercedes never had a cheap Jaguar.

83 300D Turbo with manual conversion, early W126 vented front rotors and H4 headlights 401,xxx miles
08 Suzuki GSX-R600 M4 Slip-on 26,xxx miles
88 Jaguar XJS V12 94,xxx miles. Work in progress.
99 Mazda Miata 183,xxx miles.