Alright, this will be answered using MATH estimation. Remember you need at least 200 friendship to do this. First, to solve how long it takes to run 1000 steps:
About three minutes running in a circle. Hold your left stick right and your right stick left.
1000 steps = 5 laps around the mesagoza typing circle. It takes like 2 minutes.
Source1
Alright, so about 2-3 minutes to run 1000 steps. Now how rare is it to get a Partner Mark?
Partner Mark: 1 in 100 every 10,000 steps
Source2
So you have a 1 in 100 chance to get this mark every 10,000 steps, or 20-30 minutes.
So the chances are you should get the mark after doing this 100 times.
100•(20-30 minutes)
You should get the mark in about 2,000-3,000 minutes(or 33.33-50 hours) if you continue to run the entire time. Hope this helped!