Hello and welcome to JustAnswer!
You most likely have a small catalytic converter for each bank on your truck, mounted just after the exhaust manifold collectors. Above these, just after the collector you will find an upstream oxygen sensor on both banks. The left bank is bank one, the right bank is bank two.
Make sure the tick you are hearing is actually not an exhaust leak. The exhaust manifold gaskets can leak on these engines and tick like a lifter. The gaskets can leak, the bolts can loosen up or break off. Look for any signs of black around them, if you see black they are leaking.
Almost all electrical connectors can be ordered from your dealer's parts department. You will most likely be able to get the replacement connector for the one you have melted.
The sensors are there for sure, it's just a matter of seeing them. There will be one on each bank before the converters. A flashlight will probably help you see them in the dark under there. Alot of times these sensors aren't in the friendliest of places.
The lifters aren't that bad to replace. All that has to be done is remove the valve cover and there is a tool to compress the valve springs to allow for lifter removal without removing the cam and having to disturb the secondary timing chain.