I pray for the dead because everything that is in me cries out that they desire our prayers.
As far as time vs eternity, I have seen cases of folks whose physical condition is changed even though, in the (recent) past, they were diagnosed as seriously injured/ill. This is “after” the prayers of God’s people. If (& I have seen this) a child’s jawbone is broken into pieces in a car crash, & people pray, & the next day, new x-rays show that the jaw is whole & normal, then God has reached into what we call “the past” & changed the case entirely.
In the same way, when we pray for the dead, they are not in time. Being beyond that limitation that we have, why would our prayers not be efficacious in eternity?
Besides, as I say, the heart cries out for the prayers for our beloved dead, as well as for ohters who have passed from this mortal life. It is not necessary to believe in purgatory in order to pray for the dead. (I do, in fact, believe that we all must pass through a process of cleansing to be ready for God’s presence, but it isn’t necessary to believe as I do in order to pray). What is necessary is to be open to the inner voice of God that speaks to those of us who know & love & serve Him, & to obey that voice.
I am a big believer that when God tells me to do something,** I had better be doing it**, and
not arguing the exact theological complexities involved in the case.
I am the servant; He is the Master. I just do as He leads me, & He leads me to pray for those whose faces are no longer here with us on this old earth.