Seeking advice on knowledge discovery
There are a lot of different possibilities. It is a bit hard to get the message through here in the forum. But I try and focus on one thing that is relatively easy to implement:

One of the easiest things you can do is to do a linear regression. You dependent variable (y) would be „fire trucks working“ (or the share of working ones). You can estimate this dependent on time. So you can (for example) generate indicator variables (=1 if something is true vs =0 if not) which indicate things like weekday, hour of the day. Use this indicators as explanatory (x) variables in the regression.

The result will be, that each indicator shows you the average truck use at some point in time. Say indicator A is „monday“, B is „16:00“, you will see how many trucks are on average dispatched in this time window. You can also easily see if the difference is significant or not.

In the past such models were used to estimate the number of callers in callcenters. The thing is called „dummy variable regression“ (at least in some statistic fields). https://en.m.wikipedia.org/wiki/Dummy_variable_(statistics)

Note that you observe effects from each „dummy“ variable in contrast to a baseline. Imagine you have truck use (y) and only 1 indicator/dummy, which is „monday“. Say the intercept of the model (the result with all dummies =0) is 5, meaning on average 5 trucks are employed. If the effect/coefficient of your dummy is 2, it means there are 2 more trucks employed (on average) on mondays. So each dummy/indicator (viz in case it is 1) shows you an effect in contrast to the base category (where all the dummies are 0).

Here is some script in Python which I guess refers to a similar problem, maybe it helps for orientation: https://stackoverflow.com/questions/50733014/linear-regression-with-dummy-categorical-variables

Also this may help: https://songhuiming.github.io/pages/2017/01/21/linear-regression-in-python-chapter-3-regression-with-categorical-predictors/

Another note: In principle I would try to get many different dummies/indicators from the timestamp, e.g weekday, hour of day, special days or seasons (Christmas, winter etc). You need to try combinations which work for you and the model. But don‘t plug too many indicators into the model. Keep things easy in a first step and try to improve the model later.

In order to check the „quality“ of your model you can look at R2 (a measure that shows how well you are able to explain the data which is between 0,1). You can also randomly (!) set aside some 10-20% of the data (do not use them to estimate the model in the first place) to check how well you model can explain real truck use at some point in time. 

I would use R for such a task (I find it more intuitive than Python). Here is some example code for R: https://stats.idre.ucla.edu/r/modules/coding-for-categorical-variables-in-regression-models/

Hope this helps: Good luck with your interesting project!