BUG: Fix Gaussian1D pickle behavior (affects Gaussian1DKernel) #18598

• Revert TST: Disable Gaussian1DKernel in pickle test due to flakiness #18596

From @eerovaher:

astropy.convolution.Gaussian1DKernel sometimes fails check_pickling_recovery() because astropy.modeling.functional_models.Gaussian1D sometimes fails it. Fixing the latter will automatically fix the former.

The fundamental problem seems to be that modeling pickling tests don't use the general astropy.tests.helper.check_pickling_recovery() utility. The big difference between modeling tests and check_pickling_recovery() is that the former compares original and unpickled data with numpy.testing.assert_allclose(), whereas the latter requires strict equality. It is not clear to me why modeling chose not to use the general utility.