Here is another vote for "it depends" and "you and your buddy should have discussed this."
Here are some factors to consider.
Under normal conditions, at 18 minutes/60 feet, a safety stop is considered completely optional until you have been under water for 49 minutes. Even if you have very good control of your breathing, if you are using an AL 80, you and your buddy will have been back on the boat rehydrating by then. We must therefore assume that your lost buddy incident happened much earlier than that. How much earlier? Well, if it happened two minutes after descending, I hope we can all agree that a safety stop would be silly. The closer you get to the 49 minute mark, the less silly it becomes. That's one aspect of the "it depends" part.
Next, as TSandM points out, if you are diving in current, the current is usually different at different depths. The more time you are at a different depth from your buddy, the farther apart you are going to be when you finally surface. In a quiet lake, that won't matter. (Another "it depends" aspect.)
Overall, on an 18 meter/60 feet dive, my strong inclination would be to head directly to the surface.
Although it is therefore important to make sure you both know the plan, more important is the willingness to stick to the plan. I have been in only a handful of situations where I have had to surface for this reason. On every case, I was with divers who knew the protocol well, and on every case, the missing buddy ignored it. In each case, fortunately, although we were in very poor visibility, we were also in very benign conditions, so it was more of an annoyance than a serious concern. In most of the cases I was eventually able to spot bubbles and swim down through them (to very shallow depths) until I found the diver. Normally what I just described is not a good idea unless you are sure it is the person you are looking for, otherwise you get the endless case of divers popping to the surface one at a time, looking around, and then descending to look again.
In one really weird case, I was with a group of 5 who were following a diver who was navigating by compass. At one point he made a sudden turn and we lost him. The 4 of us stayed close together carefully, and he later said he could hear us breathing but could not tell where it was coming from. After a minute, we thumbed the dive, which was only about 30 feet deep. We waited on the surface for him. We looked for bubbles, but it was a windy day, so the surface was rough. One of us spotted something strange--an inflated surface marker buoy blowing away in the distance. To cut to the chase, although he knew very well what he was supposed to do, he decided he had a better plan. He inflated a surface marker buoy and sent it to the surface so that we could find him. He had not secured the line properly, and it became unattached--that was the marker we had seen blowing away in the distance. What if his plan had worked? We would have gone down to find him, at which point we would have had to go back to the surface to empty the marker and continue the dive. Once he realized his marker buoy plan had failed, he came up with another one--he took a reverse heading on his computer and went back to shore. We were in a state of total concern (OK, now what do we do?) and were beginning to make a rescue plan when we realized he was on shore. The moral of the story is this: the standard lost buddy procedure has already been determined to be the best way to do it, so it is unlikely that anything you come up with while under water will be an improvement.
