These skins (among others, [[https://codesearch.wmflabs.org/search/?q=UseTwoButtonsSearchForm&i=nope&files=&repos=|non-WMF deployed]]) make use of this variable to provide two-buttons search form (see https://www.mediawiki.org/wiki/MediaWiki?useskin=monobook).
This variable (which lives in core but not used there) will be removed in T42622. Removing it directly will mean these skins to silently change behavior which will obviously be noticed by their users. This task is to decide the future of the config option in these skins. If it's decided that any of these skin want continue supporting it, then the config would be moved inside the skin itself. Otherwise it would be removed completely.
[] Monobook
[] Modern
[] CologneBlue
[] Nostalgia (this one will be simply removed completely).
[x] Other skins (advised to move the config inside the skin itself if they want keep the behavior)