Battery terminal contact problems at the battery post account for the majority of high-current problems. A first step should always be to use a battery post/clamp cleaning tool to make the sufaces shiny, then re-attach. Remove negative clamp first, replace it last. Battery post itself could also have broken internally, so replacing battery could be necessary if post cleaning doesn't solve the 'wiggle' issue.

Steve

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'91 MB 190E 2.3
'08 RAV4 Ltd 3.5
'83 Lazy Daze m'home 5.7