That 10 secs. to jump to 14V is much longer than mine. Miles said less than a second...I thought a few secs...Miles is probably closer to the truth.
Look for corrosion/looseness...
Follow the cables all around...and if you haven't done so, you can easily get to back of alt by removing airbox...I'm sure you know. Clean the connector on the plug and check that cable connection under the alt's rubber boot...you might also see whether you have a collection of leaves in the vent tube too while you're there...or blow out the back of the alt (I found a crap in mine when I replaced it)
Debut Radio Show Tues, May 3, 1 p.m. on Hamiltonradio.net The Mechanical Animals
call in for car repair help! 609-503-4058
A recent set--NSFW audio: https://youtu.be/_dcxcZfD6dg
Mangofy your E46!