A good battery tender should have fixed leads to mount on the terminals and a plug at the other end to connect to the charger itself. The age of the battery is not helping your situation with the corrosion. The electrolyte levels are probably way off, plus heavy corrosion is a sign of over charging, usually from the alternator. Because the clips from the charger are so corroded, I would have to believe that crappy little unit from HF is overcharging your battery.
Actually, I just read some of the reviews on that 14.1 V charger and this was the first one to pop up - There is nothing "automatic" about this charger, and it violates its own spec (which says maximum output is 13.2 V, when it is actually 14 V). Its output voltage is too high to be considered a continuous float charger, since the battery could be overcharged and, eventually, the electrolyte fluid boiled out leaving it dry and dead. I saw no evidence of it trying to regulate its output voltage to 13.2V using either a real (well-charged) car battery or resistive loads. Others have also mentioned that the voltage is too high to be a float charger and leave on all the time, I agree.
Other reviews stated these don't charge at all and have actually drained the battery so low, they had to buy brand new batteries. A lot of people have had good luck with HF electronics, but other people have had terrible luck. It's 50/50 chance and when you consider some of the consequences for cheaping out on stuff like this, I'd rather spend the extra money on a tried and true brand to receive that peace of mind. The reference above about draining the battery was in regards to two chargers a gentleman purchased for he and his wife's scooters. So $18 for two chargers that drained two $25 batteries, and he was over the 90 day warranty so was stuck with them. In other words, he threw away $70. Heck, even a tender from Harley Davidson is only $40 and I know that works because I've used it thousands of times since buying the bike in 2009.
When you say Battery Tender JR, are you referring to the small one sold at HF or the actual JR. by Deltran? Deltran makes good chargers and that should last. I have at least 4 different older, quality, American made, heavy duty battery tenders and chargers that I've picked up at flea markets over the years. These things are solid metal inside out and never have a problem with them. Some cheap and easy insurance while using your new charger would be to clean the terminals on the battery really well and apply some grease or vaseline to the posts, clamps, exposed wires and even the ends of the charger.
