a:hover not working

An id selector (#logout) is more specific then a type selector (a) plus a pseudo-class (:hover), so your first ruleset will always win the cascade.

Use #logout:hover instead.

Simplifying:

You have two CSS rules that apply to this anchor.

Both rules change the color.

Only one rule can apply; only one color can be chosen.

The browser has to choose between the rule based on an ID (#logout) and a rule based on the element type (<a>).

The rule based on ID wins in this situation. It is more specific to specify an ID than to specify all elements of a type (anchor).