I dilute my Oil Pro dyes with IDA (you need to register to buy it) but something like Surgical Spirit (from the chemist) still has a pretty high percentage of alcohol. Once I've applied a couple of coats and got it as even as I can, I then wrap the piece up in clingfilm and leave it for 24 hours, before unwrapping. This keeps the leather damp and seems to help the dye to distribute more evenly. I then find it usually wants another day to dry completely, and lose the spirit smell.
For Fiebings standard dyes (thought not water based), damping the leather with water has a similar result.
Alternatively, you can do what I've also seen on here, and make the uneven dyeing into a feature, e.g. by stroking the applicator in parallel lines across the piece.
Geoff