Thanks for looking into this. I am confirming with others, but to me dtype= seems working and OK to keep around.
I would say we should change the scope slightly (sorry). That is modify the signature to something like: argmax(a, axis=None, _dtype=None, out=None, keepdims=False, dtype=None)
If _dtype is not None we then give a DeprecationWarning that in the Future out, keepdims, and dtype must be passed as keyword arguments.
(I.e. the future will be argmax(a, axis=None, *, out=None, keepdims=False, dtype=None) which differs from NumPy in the extra dtype and out being kwarg only, but I think both are fine.)

We also need to make sure to do two other things:

1. If we modify argmax, we should make sure to modify argmin and the methods in core.pyx also aligned with identical changes (they may just be able to forward to a single warning).
2. Any change should get some new tests to confirm it.