Those two amps should not be drawing enough power to require an alternator or battery upgrade. I think I found your problem though:
Dielectric grease is electrically insulating and does not break down when high voltage is applied. It is often applied to electrical connectors, particularly those containing rubber gaskets, as a means of lubricating and sealing rubber portions of the connector without arcing.
A common use of dielectric grease is in high-voltage connections associated with gasoline engine spark plugs. The grease is applied to the rubber boot of the plug wire. This helps the rubber boot slide onto the ceramic insulator of the plug. The grease also acts to seal the rubber boot, while at the same time preventing the rubber from becoming stuck to the ceramic. Generally spark plugs are located in areas of high temperature, and the grease is formulated to withstand the temperature range expected. It can be applied to the actual contact as well, because the contact pressure is sufficient to penetrate the grease. Doing so on such high pressure contact surfaces has the advantage of sealing the contact area against corrosion.
Another common use of dielectric grease is on the rubber mating surfaces or gaskets of multi-pin electrical connectors used in automotive and marine engines. The grease again acts as a lubricant and a sealant on the nonconductive mating surfaces of the connector. It is not recommended to be applied to the actual electrical conductive contacts of the connector because it could interfere with the electrical signals passing through the connector in cases where the contact pressure is very low. Products designed as electronic connector lubricants, on the other hand, should be applied to such connector contacts and can dramatically extend their useful life. Polyphenyl Ether, rather than silicone grease, is the active ingredient in some such connector lubricants.