I'm a little surprised to hear that the bugs moved to other things in your garden. When I used to have them, they stayed with the squash for the season....provided there are still squash plants and fruits.

What I did successfully for a couple years was to determinedly mash [by foot] every single one of them in the early fall. It wasn't as hard as it sounds as they massed on the remaining green leaves and fruits.

Yes a few may may come back, but it isn't hard to kill 3 or 4 a season then, and if done faithfully, you may not have man y of them...I don't.

Squash bugs are known to feed on other plants besides squash family members, although more often it is Stink Bugs people see on things like tomatoes.
One strategy for control is later planting, if your growing season is long enough to do that. Placing Floating Row Covers is another. Knowing as much as possible about them helps also.

Here is a link that might be useful: About Squash Bugs

I think it is on the Veg. Forum, someone said to plant Buckwheat to draw in a fly that will kill SB.

A recent episode of Growing a Greener World was about insect pest management. As with much else about organic gardening/farming there is much more to it then just a simple growing this or that plant to attract certain predators. Take some time to watch the program linked below.

Here is a link that might be useful: Growing a Greener World 223

Floating row covers work great, but squash will have to be hand-pollinated. This is very easy to do with a little paint brush.

I spray with neem before I see any SB. Spray any egg clusters you find too. Got to get them early as usually only a few survive the winter but do the population explosion thing in a short time. Once they're everywhere it's harder to knock them down in numbers.

follow up
I had not one squash bug this year. This year I did not use the newspaper to mulch my garden Instead I used chopped leaves and not one squash bug showed up. Not sure the mulch had anything to do with it but it is the only thing I did different.