I have no secret machine for shaking the Vallejo bottles, other than a little routine.
paints that have stood still a while, as you well know, settle out: all the good stuff falls to the bottom and all the runny stuff heads for the top.
I find the colours that I will be needing and lay them down. This makes them settle out to the side of the bottle. Half the job is now done. Then its make sure the lid is on and shake the living daylights out of them. It also helps to bang them against your other hand from time to time as it will loosen any stubborn stick bits from the sides of the bottle.
I will confess that at times if there are a load of different colours in the scheme, I do tend to get a bit of a flair up of the old tendinitis.
Paint that is in tinlets is much easier. Buy some high grade ball bearings about 5mm. Clean them to get every last milligram of grease off them and pop on in each tin.
Then take a length of piano wire, about 2mm. Soften the end in a flame. WHEN COLD wrap it around a tin sized bit of dowel to form a holder for the tin. Drill a hole in the work top. (do not do this bit if you build at the kitchen/dining table). Give the tin a quick shake to get things moving then pop it in the holder. Put the end of the wire in the hole and give it a knock to start it swinging. The to and fro motion will get the ball bearing moving and the paint will mix its self.... If it slows down, just give it a push and get back to reading the forum.
Ian M (master of Heath Robinson engineering).