Should the implementation of a hybrid element as defined above fall through, an alternative is to define 2 elements (<search> and <searchform>) for the 2 use-cases:
<search>===<div role=search><searchform action="...">===<form role=search action="...">
Implementing this is trivial by aliasing HTMLElement -> <search> and <form> -> <searchform>. Corner cases of nesting need no consideration, and the specification is a trivial "Uses HTMLFormElement, as defined for form elements". The trade-off is that two instead of one element specifications are added.
Should 2 elements find opposition, the proposal would be to favor the best practice:
<search action="...">===<form role=search action="..."><search>can be used without form submit functionality by capturing the ENTER keypress on inputs in a JS eventhandler, however<div role=search>remains the suggested usage if form functionality is is to be avoided.
Implementing this is trivial by aliasing HTMLFormElement -> <search>. The trade-off is that a few use-cases of the original request is not treated as first-class. The reasoning above implies that the best practice is more important to be treated as first-class, thus if a choice has to be made it should be to favor form semantics. This proposal makes a strong effort to avoid such trade-off.