There are two distinct issues here: trademark and patent. There's also issues of the law vs. issues of good lawyers.
Fender and Gibson can't really be making a lot of patent claims for things like the Les Paul. That guitar design was introduced over 50 years ago. The maximum duration for a patent is 20 years and design patents are even shorter at 14 years. Any patents on this design has long since expired. There's been a lot of interesting inventions in guitars in the last twenty years, but much of what we see today is much older than that and patents don't really apply (see the caveat below, though).
The other issue is trademark. You can trademark almost anything, especially names and shapes and physical appearance. This is the real protection for things like the Les Paul and companies tend to be really aggressive about trademarks. And, they can be renewed indefinately.
So, in general you probably have more to worry about trademark than patents. That said, there's the issue of what's right and what actually happens. Patents are not renewable. Witness the number of generic drugs out there. When the patent expires, anyone can make the drug. Yamaha held a patent on FM synthesis, but that expirect in the 90's and FM synthesis appeared in everyone's computers. But, it's possible to play games with patents. You create a derivative invention and write you patent so it ends up covering any old version. IBM is brilliant at this, locking up a compression method for over a decade after the first patent expired by simply making a varation on the patent. The drug companies can't pull that one off, because those wanting to make a generic have lots of legal money for challenges.
Trademarks can be abused as well. Writer's Digest had a column for 20 years called "About Books". Some company came along and decided to make a magazine called "About Books". They trademarked the term and promply sued Writers Digest, who ended up having to pay a fee to continue to use the name they had used for decaded. The Les Paul trademark was applied for decades after it came out.
So, what does this mean to the home builder? I'm wondering that myself. I don't believe there is a personal use exemption on patents, so companies can go after us if they want to. The same applies for trademarks including body shapes. I would hope they would not want to bother over someone's basement project, though I would not suggest selling a copy of any commercial product (protected or not, I think that's unethical). Of course, they have to know, but forums like this may turn out to be problematic if Gibson, Fender, or whoever's legal department thinks they can churn some hours.
BTW, patents and trademarks are all online, now, so if anyone wanted to they could see what really applies during their project.