We did something similar last year - had a rental car around Seattle and had to return it at SeaTac. Ours was returned to the rental car center, so different location to you, but there was transport from the rental car center to the light-rail station.
A quick look at google maps suggests your rental car return is right next to (or across the road from) the light-rail station, about a 6 min walk.

During weekdays the wait isn't long, less than 10 minutes, and the trip to King St Station takes about 40-50 mins (actually might be quicker, according to google transit screenshot below). The rail cars can get quite full with commuters and students, but seats were easy to find when boarding at the airport.
Since you're traveling on a weekday there shouldn't be too long a wait to find a train. If you're concerned just go earlier and catch an earlier train into the city. We allowed about an hour, so would have arrived before 8:15am to get to the city by 9:15am. Probably would have aimed for 8am-ish to give a bit of wait time etc.
These are the times that Google Maps gives me for light-rail from SeaTac to King St Station (to arrive by 9:15am Friday)

I can't remember but I think there was a short walk (<5 mins) from the light-rail to the Amtrak once arriving at King Street Station.
See also Sound Transit Trip Planner with approximate details input.