What is the pKa of 2-methyl-2,4-pentanediol?
Do you mean 2-methyl-2,4-pentanediol? 

The $pK_a$ values of 2-propanol (isopropanol) and 2-methylpropan-2-ol (tert. butanol) are 16.5 and 17, respectively and I'd expect your diol to be in this range range, unless deprotonation is featured by intramolecular hydrogen bonding. In that case, the $pK_a$ might be somewhat smaller, around 15.