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My '87 owner's manual calls for 5w30 as the preferred oil. It also states 10w30 if used with outside temperatures above 0° F.
It recommends an API energy conserving oil with the designations of SF (If I remember correctly). However no current oils use this rating from 30 years ago. The ratings advanced multiple times since then.
The owner's manual does not recommend a brand. Even in later years it recommends meeting a specification but not a brand. It is confusing because many sources including GM state that the factory fill is Mobil 1 (starting in '92). Starting in '92 GM went to a full synthetic oil because they eliminated the oil cooler and the synthetic oils could withstand the heat and met the specification.
Personally I would stick with 5w30 oil and I prefer full synthetic oil.
Some people have had oil leaks when changing to synthetic from conventional oil. Usually it is because of bad gaskets and the synthetic oil can clean better and may be a smaller molecule that can find small leak paths. My '88 had this problem and I had to replace some gaskets.
Most high mileage oils have added some things to help maintain/soften seals. I question how effective they are.
For right now I would recommend Mobil 1 full synthetic 5W30. It is priced in the low $20's at walmart and others for a 5 quart jug. There is also a rebate you can find on Mobil's site that pays $12 with the purchase of 5 quarts (or 5 quart jug) (or $17 if you get a Mobil 1 filter also). You can check the rebate submission web site and I think the rebate allows for 4 rebates. So it is up to $48 if you buy four 5 quart jugs. I did this and already received my $48 rebate. I bought mine at Walmart for $22.88 - $12 = $10.88 per 5 quart jug.
Factory spec is pretty much the lowest standard till you are out of the warranty, IMO so do your research. Better yet, send in an oil sample so you know if you can extend the oil change interval and see how much it will save you. I factor in my time as though I took it to a shop. So if it is easier on the wallet, I'm in. If it can say triple my OCI but costs a bit more, I'm in. IF it cannot, regular oil will work.
I thought GM put synthetic starting with the 1992 Corvettes because they removed the oil cooler? Through 1991 (L98), they all had oil coolers... yes?
When I had my '87, I used Mobil-1 5W-30 full synthetic.
GM did go to a full synthetic oil in 1992. Because a full synthetic could handle higher oil temps, the engineers felt that an oil cooler was no longer needed. The RPO KC4 was a $110 option starting in 1986 KC4 wa installed on 7700+ 1986 models, 6600+ in 1987 and nearly 19K went on the 1988 cars. in 1989, over 20K coolers were installed. The number of coolers dropped after that, ending in 1991.