Hi There, your age would have no baring as long as you have the required stamps and at 62 I would be confident you have enough, contributions paid. Illness benefit would likely be approved immediately if your GP certifies you , my suggestion if I may, would be to get approved for illness benefit first if you are unable to work , your GP can issue a closed cert which means no need for monthly certs. The GP will only issue this if your illness will be long term, over 12 months. IB is not means tested and if awarded it doesn't stop you applying for IP. Its important to note, IB has no additional entitlements attached like Fuel allowance. Keep in mind the IP or indeed DA application process can take months and Job seekers wouldn't be an option due to the fact you must be seeking employment.
if you are giving up work, my advice is to go on illness benefit initially if you can't continue to work and also commence the application for IP immediately , if you can continue to work whilst applying for IP , fine but just make sure you have medical reports, evidence etc .