I have a 96 years old aunt who has absolutely zero political ambitions, but could do a better job of governing than most in Washington DC these days. Admittedly in the last two years in my opinion, she has had some decline in cognitive ability but she still is sharper than most of the morons in DC. She walks long distances with no cane or walker, still has her driver's license and drives herself to nearby appointments, does her own grocery shopping, a lot of her housekeeping, and manages her financial portfolio competently.
We had a very good friend pass last year, age 93. Sharp as a tack. (Died from renal failure.) His mother-in-law died at age 101 earlier this year--literally of old age. Again, sharp as a tack right up to the end. Then there are others who are mentally unfit at 50 and younger.
This is to say that neither term limits nor age limits will solve the problems with incompetent and/or corrupt government in DC. What will solve the problem is to take the money out of it--no pension other than maybe a small percentage match of deposits in a 401K only while the member is in office--ALL private business and investments must be put into a blind trust and stocks, bonds, etc. can neither be purchased nor sold while the member is in Congress--representatives and senators utilize and pay for healthcare in the same system the citizens use, members must recuse themselves from debate or vote on any issue affecting a business they own.
Do that and most will term limit themselves and go home to live under the laws they pass for the rest of us. Integrity will be restored to the government. Those who love the job can stay under those restrictions and we will benefit from their experience, but we will have true public servants in office instead of professional politicians out to get whatever they can for themselves.
And as for age, if a person is still mentally sharp at 60, 70, 80, 90, there is no reason he/she should not serve at least as far as age is concerned. But it could be a good idea for those running for high office to receive a fully comprehensive cognitive function exam in addition to a medical exam that would include testing for illegal substances, etc.