Steven; appropriate skin prep goes a long way to achieving what you are seeking.. be certain to allow sufficient time for the primer/moisturizer to penetrate ...

I've migrated entirely to airbrush and virtual eliminated the aforementioned issues...
Please be aware that you'll need to be using a significantly lower psi in the sensitive lid area... test this on the soft skin under your wrist... if it dimples the skin here you'll need to go lower, it's a delicate dance to achieve an effective product stream at close proximity to the lid (as close as one inch for ornate decor...)

Also keep in mind that guns typically used for base i.e. foundation generally have nozzle sizes too large (0.35mm) for delicate ornate work like this I've found a gun with an 0.30mm nozzle far more appropriate here...  my current fav is the Iwata HP-C Plus

hope this helps...