so if the plan is to use a pump and sealant anyway. . .
why not just leave the spare wheel as-is and just get your new pump & sealant.?
the only difference will be the slight weight increase of carrying the 16" spare - VS - having to remove and refit the bumper?
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thinking, if it was me . . . . id just cut a section of the rear bumper out with a multitool underneath, to allow access to the fitted spare, as i have no faith in air pump and goo. ( and I'm assuming you wouldn't see the cut? , and it wouldn't effect the rigidity?)
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but totally understand if you didn't want to cut the new bumper.
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options:
1- cut bumper and use fitted spare
2- remove bemper and spare - get goo and pump
3- leave spare as-is - get goo and pump