Systemd timer will not fire

I have a timer that is literally this:

foobar.service:

[Unit]
Description=Timer Test
Requires=rsyslog.service      # rsyslog is an active local service.

[Service]
Type=simple
ExecStart=/usr/bin/logger "Running foobar timer test!"

foobar.timer:

[Unit]
Description=Test Timer

[Timer]
OnCalendar=10:00              # See below about the time.
Unit=foobar.service
RemainAfterElapse=no

[Install]
WantedBy=timers.target

I tested this by installing it (systemctl enable foobar.timer) with the OnCalendar 10 minutes in the future. However, it doesn't run, and:

> systemctl status foobar.timer
● foobar.timer - Local Daily Tasks Timer
   Loaded: loaded (/etc/systemd/system/what.timer; enabled; vendor preset: enabled)
   Active: inactive (dead)
  Trigger: n/a

It claims to be loaded and enabled, but inactive (dead). This is especially perplexing since I've written other timers following this pattern and they all work... o_O?

I've done everything short of rebooting the system (which I don't like to do, it is an active server).