Hello David Littel,
unfortunately this configuration would not be possible. You can choose external clock mode 1 and clock the timer with signal connected connected to TI1 or TI2 pins, but then you cannot use other slave modes as trigger or gated mode. You can combine different slave modes with external clock input in timer that have ETR input and are capable of external clock mode 2. Please see chapter 2.4 of AN4776. Maybe it would be option for you to use EXTI on the specific pin and program interrupt routine that would reset the timer.
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