Do yo feel it’s better to take check at 62 and continue to supplement, part time etc, or wait as long as possible?
Why wait? Get something out of the system early, because you may croak before you get to full age. Those years of receiving reduced payments make up for waiting for full payments, unless you think you'll live a very long life. Hopefully one has other sources of income and savings, in case you do live long.
Your life expectancy is the key factor imho.
If your family tends to die young, take the money asap, cause you can’t take it with you.
If your family has very long life (into their late eighties or later), then you want to wait as long as you can afford to do so.
Wait until full retirement age. The difference pays off in 5 years IIRC. But waiting after full retirement age takes 14 years. But taking it early is a disaster if you live into your 80’s or 90’s.
You must also factor if your spouse is taking a spousal benefit or their own. If the take a spousal benefit the above changes.
Best advice on the web is Jonathan Clements
Follow this link and then find the section labeled “ACT”.
https://humbledollar.com
This guy is really good on finances and retirement.