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Let's look at what we know. First off, in A Tale of Two Stans, Ford called McGucket "a young but brilliant mechanic". This implies that at the time of his flashback, McGucket was the same age as, or younger, than Ford. Ford is supposedly currently in his 60s, which means that during the flashback, he would have been in his early to mid 30s. Let's assume that Ford meant that McGucket was the same age as him. Now here's where it starts to not make sense. We know that McGucket and Ford worked together for nearly a year. We also know that after this year, he used his memory gun rapidly. McGucket cleared his mind commonly, and his physical appearance suffered as well. It is supposed that McGucket completely lost his former self by July of 1983. However, in Society of the Blind Eye, it it shown that he had his current, long, grey beard that he still had during the show. If McGucket had truly been the same age as Ford, he would still have been in his mid 30s. It is very uncommon to grow a beard that was as grey as McGucket's during your 30s.
This is what I think. I think that McGucket was lying about his age to Ford because he was embarrassed about going to such a low-level college. He likely used hair and skin products to make himself seem younger than he really was. When he went crazy, he likely stopped caring about his appearance and stopped using the products. He allowed a long beard to grow, which became all grey and appeared as if he had been older. Hair generally starts greying in your 50s. This means that it is likely that if McGucket was faking his age, he would have been in his 50s in 1983. Furthermore, if he had been faking his age and had been in his 50s during the flashback sequence, he would be in his 80s during the show. This is my theory for McGucket's age.