Are you kidding? How is prayer not a work? Jesus sweat great drops of blood when He prayed (hematidrosis). That is indicative of great effort. The Greek word usually translated prayer (aiteo) literally means "ask." If you asked someone for help in changing a tire, would that act of asking not be a work? Again, prayer takes time; it is a progressive act. Belief is not progressive.
The Bible says about Anna that she "served God with fastings and prayers night and day." (Luke 2:37). The word for "served" there is clearly a work.
John,
Perhaps it is that the prayer of salvation is that first offering of thanksgiving in response to work done and not the initiation to work done. I present that is the larger significance.
For example, while traveling across country a number of years ago, I was following a car of an elderly that I saw had lost air in a tire. Becoming aware of the flat, they pulled off the road, and I stopped behind them. Walking up, I introduced myself and said, "I would be glad to replace your flat with your spare." I didn't offer to help, I stated that I would help.
The elderly person was not embarrassed to respond with gladness, gratefulness and thanksgiving.
Such was the prayer(s) offered at the salvation of one introduced to Christ by your Grandfather.
Certainly, there is work involved. The hearing ear, the open heart, the enlightenment of the understanding, and the impress of the need. But the "asking" is that of expression, not of determination - that is prayer is the expressions of thanksgiving resulting from the actions of other work done by the Holy Spirit - conviction, righteousness, and judgement, and by the willing ambassador who "preaches" the message.
Perhaps one of the problems with this topic is it seems to bring out those that perhaps contend if one doesn't present some kind of "sinner's prayer" in which the person must ask for salvation, then one isn't saved.
No such prayer was ever presented in the NT after the resurection. Rather, the presentations of those who came to the Savior after the cross and resurrection was that of recognition and thankfulness. Prior to the cross, that was not the offer made to folks. One had to come to God under the old covenant of asking, seeking, finding. Now, believers are ambassadors who carry the message to those who do not seek. Believers are not high priests waiting for folks offering acceptable sacrifices; rather, believers are those sent out to compel others to come.
This post is not so much in disagreement with you as it is showing a bit of different hue to the thread.