The documentation of systemd (https://www.freedesktop.org/software/systemd/man/systemd.timer.html) claims that the "Persistant"-flag is ignored if the timer was not configured with OnCalendar, but I found out that this is not always the case, and setting Persistent=true can break a timer.
I tested the script below on two nearly identical machines: On one machine, both Persistant=true and Persistant=false results in a working timer, but on the other machine, Persistant=false works, but Persistant=true does not.


$ systemctl --user list-timers
NEXT LEFT LAST PASSED UNIT ACTIVATES
Fri 2020-07-24 20:29:16 CEST 59min left Fri 2020-07-24 19:29:16 CEST 32s ago test_false.timer test_false.service
n/a n/a Fri 2020-07-24 19:27:24 CEST 2min 24s ago test_true.timer test_true.service


reproduce.sh:
systemctl --user disable --now test_true.timer
systemctl --user disable --now test_false.timer
systemctl --user clean test_true.timer --what=state
systemctl --user clean test_false.timer --what=state
sudo cp test_true.service test_false.service test_true.timer test_false.timer /etc/systemd/user/
systemctl --user enable --now test_true.timer
systemctl --user enable --now test_false.timer

test_true.service and test_false.service:
[Unit]
Description=Test service
[Service]
Type=simple
ExecStart=pwd

test_true.timer:
[Unit]
Description=Timer test
[Timer]
OnBootSec=10s
OnUnitActiveSec=1hour
Persistent=true
[Install]
WantedBy=timers.target

test_false.timer:
[Unit]
Description=Timer test
[Timer]
OnBootSec=10s
OnUnitActiveSec=1hour
Persistent=false
[Install]
WantedBy=timers.target