Where is "Penis" (1965)

There's enough other sites corroborating its existence that I believe we can rule out this possibility. Just from a quick cursory search on Google we have:

1. A Published Book from the American Film Institute circa 1997 which mentions Penis in its index.

2. A foreign film aggregate site with an entry for the movie.

3. An entry on Movie Chat forums.

4. An entry on film web.

5. Yet another foreign film aggregate site with an entry for it.

^This is just skimming the first three pages of results on Google. IMDb is pretty good about vetting its entries. I'm a film buff and I've been using that site and others to discuss films since the mid-2000s and I've never heard of a fake IMDb entry happening before. But even if we allow for that possibility, its verification on other sites and especially the AFI book should be proof enough for anybody that this existed at some point. AFI is a very reputable source on filmography, I can't believe that they would just make up a movie for laughs or triple check an obscurity from IMDb to be certain. Plus the book was written early enough to predate a lot of the internet meme/"for the lulz" culture. Back in the 90s, more people were on the internet to genuinely disseminate information than to troll people and cause mischief. 

You may be right. A big problem that compounds this film's obscurity is the fact that its title is a single, commonly used word. Another is that its director shares the name of some football player. That means the only way to filter out the noise is to use both terms in your search "AJ Rose Jr" and "Penis 1965." That comes up with just a handful of results on google and besides those I already listed, I only found one other, which just parrots the IMDb information.

I guess our best lead is to contact the compilers of that AFI book and ask them what their source of information was. I know this group tends towards nostalgia and childrens media but I think this film deserves a lot of attention considering its about as lost and obscure as I've ever seen a film get.

So I decided to put the TCM summary into Google to see if anything else came up, and this movie also listed on the TCM database has the exact description:
www.tcm.com/tcmdb/title/570346/The-Lost-Handbag/

Also there are a few other movies with that same exact description.

There's actually one other lead. The TCM link has Film-Makers' Cooperative listed as the distributor. Luckily, they seem to still exist. I couldn't find anything about Penis in their archives, but I'm gonna shoot them an email because I'm curious about this now.

Well, AFI got back to me. They were very nice and supplied me with their database records for the film which didnt contain much. They also said they no longer archive "sex films" so they have no copy of the it anymore.

Although if Penis is a sex film, then chances are AJ Rose isn't this person's real name.