If you do not think this new job situation is acceptable, and you think there is some EEOC age discrimination issue, quit before you work at the reduced hours without benefits, even for one week. Working in this new position signifies acceptance of the situation. So then if you quit two or three weeks later, due to the insult, you probably would not be considered to have a good job related reason to quit for unemployment purposes.
But if you quit after you were told of the change, and you do not work the reduced hours, even for one or two weeks, then it may be seen as an effort to force you out, and you can file for, and probably have a pretty good chance of getting unemployment insurance.
But consider, if they can show that they are reducing hours across the board, due to the company's needs, stress, financial situation, not just as a mean-spirited effort to get you to leave, then you would not qualify for unemployment. And you'd be unemployed, at 60, where statistics indicate a poor prognosis for finding another good job.
There's another possibility. Go on and work the reduced hours, and file for unemployment benefits while you are still working, saying your hours have been reduced. If your hours have been reduced down to the point where you earn less in gross wages than you could draw in a week's unemployment benefits, then you are going to be able to draw partial unemployment while still working. Your state has a really high unemployment payment, so figure your hourly rate x 20 hours, and you may qualify for a little bit of unemployment to suppliment your weekly reduced wages.
Usually this will motivate the employer to either go on and lay you off totally or will cause them to up your hours again. Because if your hours are cut to below what you could draw in unemployment benefits, then you are entitled to them, and this will cost the employer in tax rates.
So the question is, is this move directed personally at you? Or is it a cost saving measure, a business decision by your employer based on other factors? That the other person in your same position did not get reduced hours is rather significant.
In regard to benefits, is there a policy at your employer that a person who works less than xxx number of hours is not eligible for benefits? I would believe this would be based on your company's policies, but others will know more benefits information than I.