Is there a way to make a script wait until Part1 is close to Part2 -- OR three seconds max?

Simple version.

local maxDuration=3;--// The max time for it to wait.
local minDistance=2;--// The min distance between the parts.

local startTime=tick() + maxDuration;
repeat 
    coroutine.yield();
until ( Part1.Position - Part2.Position ).magnitude <= minDistance or startTime - tick() <= 0;
--// Code continues.

How it works:

maxDuration is the maximum amount of time it will wait.

minDuration is the minimum amount of units the of the magnitude.

startTime is the current time added by the max duration.

coroutine.yield() is a faster version of wait( 0 ).

startTime - tick() is the time the loop started subtracted by the current time. If it is 0 or less, it will stop. (a countdown)

One way we could do it is something like a promise -- two things race to trigger the same thing and then come to a conclusion "together" (based on the results each gave) (in this case, it's just ignore the second one)

local isFirst = true
function dothing(close)
    if isFire then
        if close then
            -- Parts were close before three seconds
        else
            -- Three seconds elapsed first
        end
    end
    isFirst = false
end

spawn(function() wait(3) dothing(false) end);

repeat
    wait()
until (one-two).magnitude < 2
dothing(true);

Usually I wouldn't opt for this approach. I would try to write them in one loop:

local stopTime = tick() + 3;
while wait() do
    if (one - two).magnitude < 2 then
        doCloseThing()
        break
    end
    if tick() > stopTime then
        doTimeThing()
    end
end

local num = 3 -- Time You Want
local close = false

for i = 1,num do
if (part1.Position - part2.Position).magnitude <= 2 then
close = true
break
end
wait(1)
end

--[[ Close = true if parts are close together after 3 seconds]]