Hot Line or Big Strike ?
Those are rollover buttons in the grid BTW.

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Add in the human frailty of a poor memory or even worse, false memories, and it make this even harder.

Here's a couple of questions to ask. Others can add if they think of anything.
1. Small or standard size flippers
2. Any backglass animations. (Not flashing lights, .....animations)
3. Names like Gottlieb, Bally or Williams.

Grab some pictures off the internet for example such as the small flipper or Buckroo animation.

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Ok, maybe it's time to put your friend to work on this.

Below is a link to the Pinball database. Assuming you have correctly narrowed it down to a Williams, electromechanical machine, I have used the advance search feature and that link will take you to a list of Williams EM games made between 1967 and 1977.

http://www.ipdb.org/search.pl?gtype=EM&mfgid=351&sortby=date&searchtype=advanced

If he doesnt spot his game there and you come up with new search criteria, let me know and I'd be glad do another search base on the new info.

Also found a Gulfstream but I don't think this is it without the orange buttons.

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I believe he said he "played" it in 1974. It could have been a routed game of that year or any number of the years preceding.