What are the Gym times needs for Medals?

To the best of my knowledge, time holding a gym doesn't give you any progress on gym badges. First time you spin a gym photo disc, feed a berry, attack it or place a defender you get an empty badge. There are actions that grant you points towards badge level (bronze, silver, gold).
Putting a defender gives +100 badge points. Feeding berries, fighting, etc give you a variable number of points (no idea what's the formula here).

There's another different medal which does count time holding a gym (the sum of all the gyms you defended). For the gold medal you need a total of 1000 hours.

Please, someone correct me if time holding a gym accounts for badge progress.

Feeding berries to your mons in a gym and spinning the photo disc gives you badge "rep". Knocking down a gym gives you the most rep but obviously takes longer to do.

Holding a gym contributes to the badge and I read somewhere you need to hold it 29 days for the gold badge.

You in fact do gain experience by having a 'mon in the gym, 1point/min for a total of 1440points/day. If you're relying soley on holding the gym for the time required to obtain the gold gym badge...

Bronze: 500p; 0.35days
Silver: 4,000p; 2.8days
Gold: 40,000p; 27.8days

Additional points can be obtained by fighting at the gym at the rate of 1% of the defender's CP awarded (ie, a 3,000CP defender will award you 30p towards your badge upon defeat), 100p for adding a defender of your own, 10p for every berry fed and 1,000p for a succesful Raid.

I am currently unaware if spinning the photodisc provides and experience towards your gym badge.

Source:
https://www.reddit.com/r/TheSilphRoad/comments/6jg2mv/gaining_gym_badges/

They should make it so that once you have to gold badge you can put in a 3000CP mon and it won't lose motivation as fast.