Automake would think the target was out of date every time because e.g. '.deps' was updated.
Note: I am assuming that secp256k1 depends on *.h, *.c, and (it's libsecp256k1-config.h.h so already included), aside from pre-existing include/*. If there are other files that would require a rebuild of the LIBSECP256K1 target, they should probably be added.
It would be neat if you could exclude specific files, rather than split it up like this, but it doesn't seem possible (https://www.gnu.org/software/make/manual/html_node/Wildcard-Function.html#Wildcard-Function)
Should probably note this:
$ V=1 make check VERBOSE=1
Making check in src
make[1]: Entering directory '/home/user/workspace/bitcoin/src'
make[2]: Entering directory '/home/user/workspace/bitcoin/src'
make -C secp256k1 libsecp256k1.la
make[3]: Entering directory '/home/user/workspace/bitcoin/src/secp256k1'
make[3]: 'libsecp256k1.la' is up to date.
make[3]: Leaving directory '/home/user/workspace/bitcoin/src/secp256k1'
make check-TESTS check-local
make[3]: Entering directory '/home/user/workspace/bitcoin/src'
make[4]: Entering directory '/home/user/workspace/bitcoin/src'
make -C secp256k1 libsecp256k1.la
make[5]: Entering directory '/home/user/workspace/bitcoin/src/secp256k1'
make[5]: 'libsecp256k1.la' is up to date.
make[5]: Leaving directory '/home/user/workspace/bitcoin/src/secp256k1'
PASS: test/test_bitcoin.exe