My question is: Do villagers master fishing based on the number of fish they catch or simply the amount of time that they fish? In other words, if you put two villagers on fishing at the exact same time, and they both work the exact same real time, but one is a "runner", will that villager master fishing sooner?

I say the amount of time.
And I'm not exactly sure.

That's not correct, BW. Mastery is based on the number of successes a villager has at a task. A runner will always master a skill before non-runners (barring extended sickness or reassignment to another skill), since they complete many more repetitions of a task in a specific amount of time.

Ohhhhh....
My apologies.

To speed up people gaining skill, you can always just put a villager onto a task, wait until it says at the bottom of the screen "this villager improved at X!", then stop them and put them back onto the task.

This means that they will gain skill, but they don't need to walk the whole length of the village to get it, and you won't need to worry about whether they are a runner or not!

Thanks all! I'm trying to make a "slow-moving" elder an EE.

No wonder its taking so long for you

Fishing is not a good way to go about it! Nor is collecting coconuts. Both entail long walks and so take the elderly a long time. If you spot the villager going fishing drop him/her on the vegetable patch instead. Even if there are no crops they will gain skill by planting crops or watering the field, and the walking time is much less.