As a one time electroplating chemist and company owner, I wouldn't recommend a DIY approach to gold plating clock parts.
As Mick says the preparation prior to the gold deposit going on is critical and exacting; there is usually an intervening bright nickel coating involved. There are also many colours offered in plated golds, you may want to have a look at samples before selecting one. Wear resistance is also a factor that needs be addressed.
None of this is easily done by the amateur.
Your easiest approach is to contact a manufacturing jeweller or small plating outfit. Brmingham used to be full of them.
Eugene