mmm, later style switches.
IIRC with the earlier switches, the upper chromey bit latched onto the black rectangular housing below. You could pry them off and clean the switch innards, but risked breaking the little tabs that held them together. Once those tabs broke, your options narrowed significantly to whatever form of superglue you had in your back pocket.
You may be able to closely examine the "chrome" piece that broke off and see the little pockets where the body used to snap on... or not, these being the later switches; but BMW frequently re-uses designs and little that is truly new comes down the pike, particularly in closely related old-timey stuff like these. Something a little less permanent than superglue may be your friend here; perhaps a PVA (wood glue) which doesn't dry quite hard, will help if sparingly applied. Remember the body of the switch is still a pretty tight fit into the brushed stainless strip.
(edit) Shoot, off on a tangent, forgot the original question... there was a shiny U-shaped metal strip that fit on three sides of the black body, front to back, and bowed out slightly, making the switch a spring fit into the hole. Your question implies this bit is missing. Lacking that actual bit, or if the holes where it clipped on are no longer capable of holding it, anything you can add to the front and back of the switch body, such that it becomes a snug fit, should be enough to keep the switch in position. There are only the wires below which might press the switch up and out; if they are properly stowed the switch should stay in place almost by itself.