If he really doesn't want to pay towards a college fund, he should do whatever he wants with that extra money (pay down mortgage or whatever) and then instead of using a home equity loan to pay for college he should just take out federal loans for the college and pay those for his kid. A home equity line of credit runs around 7.25% right now? A federal student loan can be had for around 3.0% to 3.5% in most cases. No brainer. Why pay 7.25% on someting that you can pay 3.5% on?
Of course, paying cash is even better, which is the advantage of the college fund (which you earn the interest on until you spend it) or a prepaid college account. Even if he does nothing but put that money in a high yield savings account at 4.5% to 5.0% he'd be making a better return margin compared to the student loan. So he could just save that money and still get the student loan and still have a 1.5-2.0% margin in his favor assuming rates stay roughly the same. Either way, the home equity loan is probably the worst option from a cost standpoint.
But if they can pay off the mortgage before the kid starts school then they would have all that money to pay cash for college as they go. The idea that some people have of not paying off a mortgage because you lose the tax deduction is backwards - why spend $2000 ($24,000 per year) cash per month to save $2000 in taxes at the end of the year? Let me pay that $2,000 at the end of the year in taxes and leave me the other $22,000 in cash and I guarantee I can find something better to do with all that extra cash that won't make me the least bit sad to pay a $2,000 tax bill come the end of the year.