Went through this at the very end of 2012 after 11 "and a bit" years in same place (not quite up with your 22 years!).
I deliberately took an extended xmas break after the usual family visiting, and only started looking for a new job a few months into 2013. At first I was a bit choosy,thinking there's plenty of time, and didn't put CV's up for a while etc, silly really. Once a few months passed and I uploaded CV's I started to get a few calls (IT systems/network stuff), had a few interviews ,several that sounded almost done deals only to fall through at the last minute. By the end of 2013 I was getting a bit peeved off and the payoff money was rapidly dwindling (and I DID resist buying an ID cab, Tron etc etc when I first got the payout!). Got some contract work early in 2014 and then got a call back from my now-current employer whom I'd had an interview with just before xmas.
All I'd say is take a bit of time to wind down, it does feel a bit 'odd' not going into work after a long time doing the same routine, but I enjoyed having the free time. I wouldn't have thought you'd have any problems getting some contract work with that length of experience with HP, so maybe a few contract positions to keep some cash coming in ,and keep the 'eye' in etc, balanced against enjoying some free time