"Search" could also be a verb, but that makes it more of a stretch (even if we envision a kind of phone called a "rules phone", there would be a singular/plural agreement problem in taking it as the subject of "search").
I.e. we naturally parse this sentence as "(Texas) Appeals (Court Rules Phone Search)" which is wrong. The correct parse is "(Texas Appeals Court) Rules (Phone Search)". I.e. at first glance we think that "appeals" is a verb rather than an adjective.
Texan Appellate Court Rules That Searching the Telephones of Arrestees Violates 4th Amendment Protections
Unfortunately that's too long to fit in the title.
Texas Appeals-Court Rules Phone-Search After Arrest Violates 4th Amendment [pdf]
(Texas) Appeals (Court Rules Phone...) nope.
(Texas Appeals) Court (Rules Phone...) nope.
(Texas Appeals Court) Rules (Phone Search...) yes.
Most of the words can not only both be verbs and nouns, but many appear to conjugate correctly as verbs when the preceding word is interpreted as a noun: "Texas Appeals", "Appeals Court", "Court Rules", "Rules Phone"*
*"Rules Phone" doesn't make as much sense, as rules are typically unable to phone anything, including searches.
.. (Appeals Court) Rules (Phone Search) After (Arrest Violates 4th Amendment) --nonsense
"phone search after arrest" is terribly confusing, though "post-arrest phone search" is clunky.
"Appeals Court" is probably the strongest 2-gram in the headline:
https://books.google.com/ngrams/graph?content=texas+appeals%...