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To summarize,
You get a boost with an open installment loan and an aggregate balance <9% of the original loan amount. You should see that when your car loan is 91% paid off. If you had a 60 month loan, 9% of 60 is 5.4 months. So, if you pay it to 9%, you should have about 6 more payments. You will get the boost (I found it was 30-40 points) for those 6 months. As @Patient957 suggested, during that time, you could take out a ssl to kick in when the car loan is paid. If you take out another car loan or personal loan in the future, you'll lose the boost, since your aggregate would be more than 9%.
You can look up ssl. In simple terms, it's sort of a fake loan, where you borrow your own money. The tricky part is to pay it to 9% without changing the term. The only places that will do that are navy and penfed. I took out a $2100 loan for 7 years. I immediately paid It to $189. I now have an open loan with my next payment due in 2030. It doesn't cost much, the rate is 2% and I've only borrowed $189 net. Also, there's no hard inquiry, but you do get a new youngest account.
I think in the short term, paying down the auto loan should do it.
As far as timing a ssl, is your aoya less than 12 months? If not, you can expect a small point lose when you open the ssl. If you need score improvement for 3 months, do the auto loan and wait until month 4 or 5 to do the ssl.