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If your ClkPWM is 1MHz, and the period is 65535 (default),
the PWM frequency will be 61Hz, which we can hardly see the blink.
So it appears to be on all the time, not as bright as full on though.
I tried to change the clk to 1kHz and period to 1000 and compare to be 500.
So I could see the LED blinking.
As far as I tried, using LED_PWM_Disable() and LED_PWM_Start()
seem to be working.
When I want to add tweak on top of HAL, I'd create a new source and header
in user space, I mean next to main.c (main_cm0p.c etc), such as
LED_PWM_usr.h LED_PWM_usr.c and add additional codes in them.
Attached is my trial, with SW2, LED_PWM can be stopped and started.
P.S. I may misunderstood your point,
connecting LED to pwm_n makes LED off when PWM is disabled.