The current version of Firefly (release-2021.2.2) contains bvan's extensions to the TAP search screen for searching ObsTAP services, and, more generally, data in ObsCore format.
The design asked that a special radio button "Image Search (ObsTAP)" be displayed when a TAP service contains a table "ivoa.ObsCore" - which makes it an "ObsTAP service" according to the applicable IVOA standard.
At the moment that button seems to be displayed whenever the service contains any table that appears to have the ObsCore schema. While it is correct to offer Brian's enhanced search form for any table with that schema, the radio button should only be displayed if such a table has the standard-conformant name "ivoa.ObsCore" (case-blind matching should be used).
This is a high-priority fix.