The DMV stamp is good for a year, if they stamp a new IDP then you’re good for another year. They were making noises about not wanting to keep stamping them year after year but I didn’t have an issue doing it for near 20 years, it’s only due to difficulty getting a new IDP this year that I bothered to go and do the test.
Once you have a valid license (and insurance) there is no issue with the police, even in an accident scenario. A stamped IDP is fully valid.
Actually a non-stamped IDP is also valid if it is within 30 days of entering Taiwan. The bizzarro world with this is that the DMV put so much emphasis on entry dates for eligibility of various things that if you go abroad and come back to Taiwan you are good for another 30 days unstamped, even if you’ve lived here for 50 years! All that matters is the 30 date period after you enter Taiwan.
A word of caution once again though, your insurance may not be valid if you do not have a valid license/IDP or your license/IDP has expired. Post accident is not the time you want to find this out.