I just put a Parker PH back together and while everything else works fine, the top lever does not stay to the right when open. It then of course requires pushing the top lever over to close the barrels. What have I overlooked? Thanks in advance.

You should have a part called a bolt trip or sometimes called the lever trip. It's installed in the bottom of the frame on reassembly into a hole that allows the top portion to engage the locking bolt when it's retracted and holds it (and the top lever) in the open position). The other end of the part has a plunger under spring tension that gives it it's power when in place under the cocking slide. A tiny extension tab from the front of the bolt trip extends forward and s where the closing bbl lug strikes it and disengages it from the locking bolt and top lever,,allowing both to close and lock on the now shut bbls.

http://www.gunpartscorp.com/Ma...7750.htm?results=All
The bolt trip is #227.
Cocking slide is part #28

Sometimes the bolt trip is in there,, but the tiny spring and plunger get lost from it during disassembly and handling. It's a simple job to find a suitable coil sping and make a small plunger to get it working again.
You can see the tab of the bolt trip by looking down into the bbl lug cut out on the action table. A small projection that the bbl lug must strike to disengage the trip from the locking lug when the bbls are closed.

2152h,
You got it. In my haste to reassemble, I forgot it. Had me puzzled though. I had it in my little parts box and overlooked it. Thanks for the reminder.