My advice here comes from experience with the W126 chassis. While your set-up might be different, the engineering of many of these simple functionalities remained constant though many model cycles.

On mine, the parking break release cable was screwed into the dashboard (2 screws) and had a chain which extended all the way to a release lever further behind the kick panel. First step would be to remove the kick panel (i.e. the carpeted piece beneath the steering wheel). No idea how that is done on your SL but it's probably just a few screws and will be intuitive if you look. Then, disconnect the chain from the release lever (now that you have access) and remove the release handle from the dash (two screws for me...for you it might be slightly different but it should be easy to see).

99.9% sure that even though your plastic handle is broken you will need to remove the cable which is part of the same piece.

From what 97 SL320 says it sounds like you also have a screw or two...so I would pull the broken lever towards you as if you were releasing the parking break and then look under the lip up against the dashboard for the screws.

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1984 300 SD 384,000 Miles