12 psi at idle is well withon spec. If it is high mileage engine, chanes are it is just notmal bearing wear. I have seen several 6.5s at 9 or 10 psi idle and around 35 psi full load go an additional 200,000 miles.
You can always try draining 1 quart of oil, replace with atf. Drive for a day then replace oil pump with a new one and new oil & filter. The atf will lower the oil pressure some, but will wash out any contamination and break free any loose carbon. It is not a needed step, but may help.
If it currently has the low volume pump, replacing it with a high volume one will raise the pressure.
Years ago I was researching who makes the best 6.5 oil pump. I found out that Melling makes the oil pump for every brand out there, there are all relabels. This was verified to me by speaking to one of the engineers at melling. He said there was one company that was offering different relief pressure springs as a kit with theirs, but his recommendation was not to bother. So
You basically have two options, low volume or high volume pumps. The high volume is identified by the spacer block making the body longer- the one on the right in the picture. Notice the pickup tube may need to be reused if the one you get is for a different pan- an easy swap.
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