I am not familiar with HDPE, but I use BUTYL TAPE quite a bit as a moisture guard on lumber when one piece mets another piece or soil, like exterior fence posts, decking, railings etc... butyl tape is used to protect one piece from getting moisture trapped and accelerate rotting. In most cases the tape is compressed between members.
My experience is these tape do not adhere by itself over time and abuse from the elements.
For example, let's say you have a wood beam that's a double 2X and overall thickness is 3" wide. You take a 3.5" wide tape and place it over this double beam, you will have 0.5" of excess, or if you center the tape, you will have 1/4" excess on each end which most people will fold over to the side. Now if you were to screw down some decking over the beam, the tape will be squeezed between the bottom of the decking and the top of the beam, keeping water out. I have seen over and over again, the 1/4" that's folded over, will come apart from the side of the beam only a week later when exposed to the elements. I wonder how sticky it will stay if the tape wasn't compressed in between.
I have also used these tape on itself, for example, wrap the shank of a shovel with it a few times and left it outside for a few weeks, it does come apart a little at a time. So I am not sure how it would behave using it as a patch sealant in an area subject to moisture.