Yes really, if you have to have a truck anyways then with a short commute it is a loser to own a second commuter car.
It is a myth that maintenance costs are significantly higher on a per mile basis for pickups vs. small cars. Any additional "truck" maintenance costs are more than offset by the depreciation of the car and the need for similar maintenance on the car. I don't know if you have a gas or diesel truck but I have been surprised how cheap it is to maintain my diesel truck.
4000 miles per year from commuting will not affect truck life. The years will destroy the pickup much faster than the miles at that rate. Expect more than 200,000 miles from a modern pickup (mine is at 171,000) and you know that not many trucks are 50 years old.
You have to insure and register both vehicles whether you use them or not. What's your cost on that? I asked around and folks seem to pay about 80$ per month. Okay so you need to save at least 80$ per month in fuel to even cover the dang cost of having both vehicles in your driveway, not to mention purchase price or maintenance of the car. This month is June, in June there are 20 work days. You had better be saving 4$ per day in fuel alone just to break even.
With me so far?
15 mpg in the truck with a 16 mile commute and diesel at 4$ per gallon means I pay 4$ per day in fuel. You can stop now because you know that the car will use at least a little gas.
Let's cripple the truck farther and say I only get 12 mpg which is what I get when towing my 8000lb trailer. I log this stuff. So 16 miles is 1.3 gallons which is 5.20$ each day in fuel.
The car gets 30 mpg. That is optimistic since you aren't purchasing a new car and since this is a short commute. Today's gas price is 3.90 per gallon so that costs you 0.533 gallons which is 2.08$ per day. Uh oh, do some subtraction and you are only saving 3.12$ per day.
Bummer, you won't even cover insurance and tabs. Then you have to buy the car (which results in a monthly depreciation cost). The car is a loser.
I also put a value on driving the truck to work. I value the comfort and safety of a large vehicle. People in a one ton truck have a pretty good chance of surviving a wreck with most other vehicles on the road.
Now I also ride and race off-road motorcycles so I happen to own a street legal dirt bike. When it is sunny, I ride it to work. It get's 60 mpg. Since I already own the bike for recreation the fuel mileage benefit is all gravy and I am saving money when I commute with it.
$80/month is pretty high for registration and insurance but it does depend on location. My registration and full coverage on my car costs $33/month and half that on my truck with liability.
Also you are only including the cost of gas, not of wear and tear on the truck which will have a much higher price tag when it comes for replacement, especially if you are driving on salt laden roads in the winter time.
The overall cost of ownership of a truck is much higher than that of a car and the numbers do prove this out, especially which you include purchase cost.
If the truck is paid for and you'd like to hang onto it for a long time I'd say you'd be money ahead to buy a small commuter car in most cases not to mention for longer trips and general day-to-day driving.
And honestly how much depreciation can you expect on a sub 5k car? The truck is going to have far more depreciation by driving it as pickups tend to have more resale value, especially diesel pickups.