Mirroring the same question I posted on Mandolincafe.com (no response in 2 days):
Looking at the guitar in http://www.youtube.com/watch?v=qnXYB7yWKv8 what kind of tuners are those? I want to look at a close-up view and the video doesn't oblige. I can't search for them if I don't know what to call them, I tried linear, straight, inline, etc and still haven't found them, only rotary tuners.
See the comments below the video. It's a version of a Portuguese guitar. The tuners are probably made in Portugal since this is a rather specialized, regional instrument. Wikipedia has a general article on the PG if you search for it--a more generally used version, but the tuners look the same. Where to get them? You got me!
These are sometimes called 'watchkey' tuners, but that doesn't help a lot. They are typical of Portuguese guitars. Ron Fernandez (http://www.fernandezmusic.com/) sometimes has them. Perhaps he can find an appropriate set for you.
I never saw your inquiry on the builders/repair forum at Mandolincafe...
I put it in the tenor guitar forum, since it was a guitar, not a mandolin. The forum I wanted to put it in doesn't accept new topics, only replies.
I hadn't looked at the video for a couple days so I hadn't seen the responses yet. I have no need for them, I was just interested in what they were called to do an image search since there was little detail in the video. Linear or straight tuner didn't find them for me.
If you go to the site Greg posted you can find instruments with these heads under "Portuguese Guitarra for sale" but I didn't see any listing for the heads alone. He might get them for you if you really want them. I haven't used them but I've wondered how well the threads on the screws hold up over time.
There is another site that shows something like them here; http://www.crane.gr.jp/more/parts-reproduction/indexE.html
I don't know if he still has them or not. I think it is an elegant solution but also subject too the same question of thread wear on the screws. Of course, this is all supposing you are going to build a 10 or 12 string instrument.