Hi, I will give my experiences and learnings.
There are 2 "basic" types of sealing tape.
Putty tape. This is a commonly used sealing tape for windows, doors, cargo holes. If you pull on putty tape is will snap quickly when pulled apart several inches. The upside is, this is cheaper. The down side is, over time it can crack, separate and release from the siding. The separations are concerning as they can allow water to get in given the right circumstances.
Butyl sealing tape. This must be used on rubber roofs in all locations against the rubber roof as it works with the rubber and does not affect it. If you pull on butyl tape, it will stretch like taffy. And in 65 to 75F degree temps the taffy pull can be 6 plus feet before it thins out to a hair string and snaps. Good butyl costs more then putty tape by a few dollars more a roll. Good butyl tape will not crack for a really good long time. Some brands declare 20 years guarantee.
I do not know about the older 80's campers as I have not had one of them apart. On the newer campers, ~ year 200 and newer, this is what I have found.
On the corner folded seams, butyl sealing tape is used in the joint corners to help bond the corner to be more water tight.
On the corner moldings, cargo holes, doors, windows a "form" of better putty tape was used. While it does not get brittle hard after 10 years, it does crack and separate and can unbond leaving a potential water path.
I myself have converted to only using high quality butyl in all locations. Yes, it costs a few more dollars but the long term performance is better. Butyl when used on exposed cargo holes, doors etc has the ability to be sticky on the exposed edge and dirt can attract to it worse then the putty tape. To ofset the dirt sticking problem, on a white campers, using non leveling Dicro caulking will create a non tacking washable and good bond over the butyl. This is not the cheap way out, but it has longer lasting , many years worth of no worries.
I have found many different brands of butyl. Some good and some not so good. It comes is different colors. White is popular, however gray and black are also choices. You cannot tell the make up of butly or putty tape by color alone. The taffy or non taffy pull gets you in the right family of sealants.
I have found Dicor brand butyl to be very good. I use this on the rubber roof and corners. This is not what Sunline used as I cannot locate that brand. My only knock on this is it is thin even thought it states 1/8". I can only find it in 1" wide. Their part number BT-1834-1 Here is the spec's. Notice the 200% elongation rating. That is the taffy pull I amd talking about.
Butyl Seal Tape | Dicor Products | Official Website
I have also bought and used this product. I find it very good for windows, doors, cargo holes etc. Permatite 250-H Butyl Rubber Base Tape no DS5289 that is 1/8" x 1 1/4" wide. They make narrower if you like
Bought a case of it here: The shipping packaging from the factory was exceptional. Zero damage.
Here is their site Permatite Tapes, Sponges and Sealants
I called and talked to them to make sure the application was correct.
I have bought other butyl tape, pulled like taffy but a year later it turned hard and crusty. It seemed to be hit and miss on the RV sites that do not declare a brand and part number so I gave up on those sites unless I know for sure the brand and part number I can call and confirm.
In 2003 Sunline sent me some of the butyl tape they use on a roof vent warranty issue. I still have part of a roll in the basement. It is still pliable and sticky like the day I got in late 2003. I wish I knew the brand.
I do not know what you tell you if what you have is good or not. If it does not pass the taffy pull test, then I would say no to start with. Not knowing what it is, I cannot tell you if it is good or not.
Hope this helps