If you want "off the shelf" canned solution then this is a good start with a focus on possibly these units in a 12 VDC version. I only suggest Macromatic because I use them, I also use units made by ATC (Automatic Timing & Controls). There is no shortage of units like this out there off the shelf depending on your location and distributors local to you. Many use the industry standard 8 or 11 pin bases like I linked to but your call on that.
Here's an off the shelf timer for $18 Altronix 6062 Timer Module contacts rated at 8 amps.
It's an Altronix they have a pretty good selection of stuff, we used their 24-7 timer for a few projects and have been very satisfied.