Open and Close Circuit automatically (Automate Push Button)
A good start for this sort of project would be to use an Arduino.

They are micro-controller made easy for beginner to use, with a lot of community and code example available.

Learning Arduino will be a bit more difficult than using a device as you suggested, but it will open a bunch of new doors into different projects you would like to make on the future.

You can program the Arduino to give you the 0.2 sec signal to a pin, and then you can use a relay to replace the push button.

There is probably better than the relay, but we would need a little bit more what this button action controls.