Excellent question. Ultimately it's up to the voters of the state and I think it should remain that way.
Beyond all that, America isn't ready to deal with the disability issue. As a nation we can't deal with disability justly on general basis. Look at the levels of unemployment and underemployment for people with disabilities. Shameful. That represents national attitude as whole. When it the last time you saw a disabled newscaster? Bank manager? Grocery store manager? Sales person? Doctor? Meter reader? Elected official? Rock star? Dentist? Mechanic? School principal? IT person? Yeah, one or two, maybe. As a nation we must first address where we stand regarding real equality for people with disabilities before we start talking about elected officials.
Where is the evidence that Gifford's intellectual ability and reasoning is impaired? There is none. A huge mistake people often make is to assume that speech or lack thereof is an indicator of intelligence. That's not correct. Language in fact is NOT a precursor to intelligence. Speech certainly is not. How then would disqualify Gifford on the basis of disability? How then would disqualify anyone on the basis of disability? If you are elected, then you are sent by the people.
You want candidates to take IQ tests? You want elected officials and staff to take periodic drug tests? Start with that. I'm certain more than a few elected officials perform their duties hungover and wasted. Let's start with them.