The trick is patiently and carefully lining up the little pointy ends on the base of the mirror with the indentations on the base plate which is attached to the roof. If both points are lined up precisely, little force is needed. Don't try to muscle it in with a hammer or anything. It'll almost click right in with a bit of upward force.

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'89 300E - 153k miles - California car - Black/Palomino