Timing Yourself To Determine Gear Ratio/Torque
The gear ratio is simply the ratio of the number of teeth on the two cogs. If you can see the gears, you can compute it by counting the teeth and dividing. If you can't see the gears (e.g., an IGH), just measure how many times the rear wheel turns for one turn of the pedals (or, for more accuracy, do ten turns of the pedals and divide the answer by ten).

Time trials would be a terrible way to compute the gear ratio since there are so many uncontrolled variables and confounding factors. For example, a higher gear ratio would potentially give you a higher top speed but it would take you longer to get there.

It's not clear to me why you think that computing the gear ratio is important.