My horse's mane is a crazy mop top. It doesn't seem to lay on one side!
A condition I am familiar with.
This is perhaps every rider's pet peeve about manes - they lay to both sides and are wacky crazy flopping around. Generally speaking, a thinner mane is easeir to tame that a thick one. If you need to, you can pull the mane before you start the taming process to assist you.
You have a couple of choices here. The easy ways are to use a damp towel as a "hat" while you groom the rest of your horse. Moisten, and just lay over the mane. Some horses will shake off the towel so this may not be worth it.
You can also take your very stiff, short bristled nylon brush and dunk it in water. Use this to brush the mane down. You can wet the mane down and then add some "horse underwear" so the nylon holds the mane down as it dries. Doing this day after day will help, but you may need to break out the big guns.
The sure fire way to tame a mane is to put in some teenie tiny braids.
And when I say teenie, I mean it. Grab the smallest section that you can handle, and pull down tight and hard. Throw in a few crossovers of plait, and then secure with a band. You don't need to braid all the way down. If you are lucky, your horse will not rub them out overnight. Leave them in as long as you can - you may need to redo them daily. Some horses need them in for weeks at a time. Be patient and diligent and work at it every day. You may also find that wider looser braids do the trick for your particular horse. I personally like the little ones, but your horse may object. Sometimes you need to play around to see what works best. You may have to do a combo of lots of little things - wet the mane, braid it, use a neck cover.
A note about what side of the neck braids should lay on. There is no written USEF rule that says hunters must be braided on the right. But, the tradition in the hunters is strong, there's no way I would send a hunter into the ring with braids on the left. Other disciplines sport braids to both sides, using the horse's natural mane lay as the guide.
When you are taming a mane, think marathon, not sprint. Every bit counts - and work on it every day!