That is a sliding safety.

It is similar to but not the same the sliding safety found on British MH MKI before they were modified.

The so called Creedmore target Peabody Martini as well as the first model Turkish Peabody Martini's had the same MKI feature.

Never seen one that worked very well and definitely don't trust them. Trigger on one I have handled would not qualify. Safety on pull trigger, gun does not fire. Move safety off and the gun fired...