GH-48594: [C++][FlightRPC] Fix ODBC CI Long Build Time Issue #3924

Job	Run time
check-labels / Check labels	26s
TEST ONLY AMD64 Windows MSVC GLib	11m 46s
JNI macOS	10m 5s
AMD64 Ubuntu Meson	9m 47s
JNI ubuntu-latest amd64	37m 43s
AMD64 Debian C++23	6m 18s
JNI ubuntu-24.04-arm arm64v8	30m 56s
AMD64 Alpine Linux	39m 56s
ODBC	40m 44s
ARM64 Windows 11 MSVC / windows	21m 17s
report-extra-cpp	0s
	3h 28m 58s

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