Dear Paul,
I'll bet your question has a few of my readers asking, "Did he write in to brag or ask for advice?" You did great work as a couple in whittling down your outstanding debt. I don't think everyone should emulate what you have done, but the financial discipline it takes to get to where you are is inspiring.
A home equity loan is different from a home equity line of credit, or HELOC. I think you're actually asking about a HELOC. A line of credit can be a better financial backstop because with a line of credit, you don't have to borrow the full amount upfront, as you would with a home equity loan. And, during the time period you're allowed to draw on the line, you can actually pay it down and then reborrow up to the limit of the line of credit.
It's best to take out a HELOC as a precaution before you actually need it. You wouldn't want to try getting approved for one when you're both laid off from work.
The downside of a HELOC is that it is an adjustable-rate loan, typically tied to the prime rate of interest. As the prime heads higher, so does your interest rate. After a 10-year draw period of interest-only payments, the typical HELOC becomes an amortized loan requiring a monthly payment of both interest and principal.
In recent years, homeowners using a HELOC strategy as an alternative to an emergency fund have seen their credit lines reduced substantially by lenders who have cited declining home values. How probable that is going forward in your real estate market is hard for me to say.
I'd rather see you build an emergency fund as your financial backstop than to count on tapping a HELOC for financial emergencies. Three key differences are that an emergency fund doesn't have any closing costs, minimum drawdowns or monthly payments. You could always split the difference and use a little of both approaches for your rainy-day expenses.