Way to go, xausa - ML's are great fun, for target and for hutning. The jaeger is one of the very best designs for a hunting rifle.

If a true .62, I'd be using a .615" ball, .610" at the smallest.
Once the ball becomes .010" smaller than the bore, accuracy does decline as you go smaller yet. The larger bores are a bit more forgiving in this nature, than smaller bores are. My bro uses a .595" ball in his .60 Jaeger, a .495" in his .50 Virginia, and I, a .684" ball in my .69, .395" and .400" in my .40, .445" in the .45, for example - all with the same 10 oz. denim or thicker patching.
Thankfully, animals have large X rings and smaller balls can work - however, thickness and integrity of the patching becomes critical with heavier loads as pressure builds. The higher the pressure, the tighter the conbination has to be.
When working with nromal .020" to .025" patching, a ball that is no more than .010" smaller than the bore will usually be found best. We use 10 ounce denim, about .0215" to .022" for balls that are .005" smaller than the bore - with excellent results on the range and hunting.

Weak ball/patch combinations are the reason some guys have to wipe their bores often, or even between shots, just to load.

Smooth & radius the muzzle's crown with emery underneath your thumb, and use a descent ball/patch combination. Cleaning the bore is for after all the shooting is over.

Here's the muzzle of my 14 bore, showing the 'crown'. This allows me to easily load the .684" ball with a 12 ounce denim patch. That patch runs .025" measured with a mic. and .031" measured with calipers. I use mink oil for hunting and spit or water based lube for target shooting and plinking. My powder charge for hunting is 6 drams 2F.
Note the smooth, almost polished crown- there are no sharp edges to push lead ahead of the seating process. The ball swages into the bore, for a tight fit. I've shot then picked up and shot again and again, 5 shot groups using the very same patch for each shot and still achieved the rifle's best accuracy, which is 1.2" to 1.5" for 5 at 100 meters off the bags- and using only the rifle's express sights.