Sorry, I wasn't quick enough to edit the above.
Briggs and Stratton require a 6-digit (Alpha/Numeric) Model number, so when you only noted 5 earlier, there was one digit (or letter) missing.
Note: Some of the early Model numbers only had 5 digits so, in these cases, you need to add a zero "0" in front to make up the 6th digit to allow a search.
You can save and use this link for future engine searches:-

http://www.briggsandstratton.com/us/en/support/manuals/engine

The above search uses the 6-digit model code and the first 4-digits of the Type, then you pick the engine relative to your final code number.
In your case, you enter 12H802 in the Model search box and 3123 in the Type search box and press enter. The result will give you two engine variations. These being 12H802-3123-B1 and 12H802-3123-E1.
Your engine is the first on the list and you can download the Illustrated Parts List and/or the Operators Manual specific for your engine.

As an extra bit of information, the Engine Code 03060259 is the date and factory of the engine. The date in the first 6 digits in YYMMDD format, being 2nd June 2003, and the last 2 digits are the factory, being Factory 59.

Hope this is of assistance.

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