You need to give us more of the FUNCTIONAL specs and what your looking to archive..
As it stands you have already defined the technical outcome... Yet there could be many others..
In addition... Stand alone dual mode counters that give the dif and overall time are available... Some use a single display and depending on how you run it... You then scroll through to look at the different times etc... A trip timer in effect.. Rally car drivers know all about them.
If you want it built in *and *auto triggered etc... *Then depending on what inputs are available (every machine / model could be different) this will add to the level of complexity...