Hmm, for auctions I think you really need to also the other agents into account (auction theory builds on game theory). The stopping-time model doesn't have strategic interactions.
If your rule of thumb says that you should only start bidding after a third of the auctions are finished, I hope you see that there's a pretty obvious way for others to arbitrage against you.
Auction theory studies both optimal bids and optimal auction designs - imho it's one of the more useful areas of economics: https://en.wikipedia.org/wiki/Auction_theory