That cranking sounds a bit slow to me. I recall when I replaced my starter motor I was surprised at how quickly it turned over to what I had grown used to
How old are the battery and starter motor?
If you can crank for 30 seconds straight it is probably not the battery though
I had a similar issue some time ago. It turned out to be my trailer plug. This is pretty easy to check, as you can unplug it from the harness under the back of the tray and reconnect the harness without it. If this stops the issue, you can get a new trailer plug and wire it in.
I did, and as I recall it was the pressure plate diaphragm spring. This was around 10 years ago and I didn't fix it myself so my recollection my be fuzzy
When it's cold, perhaps try scrunching some newspaper in pushing it into a few spots you suspect it could be coming from. Soggy paper should help to home in on the source then hopefully. Just remember to pull it all out again 😄