caps can be bad in a couple different ways, the most common which is to have damaged or dirty rubber seals, causing them to no longer hold pressure. i have heard of caps that wouldn't open until a much higher pressure than they're designed to, and in some cases resulting in blown hoses, radiators, heater cores, etc.

when the coolant heats up, it expands. if it doesn't flow some coolant into the overflow bottle, then its either too low on coolant for the radiator to be full by itself when hot, or overpressurizing the system but without the cap opening.

how it should work is that as it heats up, the system pressurizes the cap allows some fluid to move to the overflow bottle, maintaining the specified pressure in the radiator. as soon as the temperature starts to drop, so does the pressure. in most cases they system will be depressurized within 15 minutes of a shutdown, and will suck coolant back in from the overflow bottle as it continues to cool.
because of this, anytime you want to open a hot cooling system, grab the upper radiator hose to feel the pressure inside. if its firm, wait, as opening it will cause a steam explosion and likely give you some severe burns. but as soon as the hose is soft, there is no pressure, so its safe to open.
considering all this, it appears your quick check was after the truck had been off for a little while, so the lack of pressure is to be expected.

the other way you could be not seeing any water in the overflow is if the overflow tank or hose has a leak, check it by filling the overflow full of water and letting it sit overnight. if its not still full in the morning, then you have a bad tank there.