[Update] I have found the timepulse output!
The U-blox PCI-5S is the cheapest GPS module on eBay right now (although you have to buy an additional antenna).
At first glance it seems useless for microcontroller projects because it's a mini PCIe card, but as it turns out it has an easily accessible UART port that can be connected to a microcontroller.
Here's the pinout:
RX/TX pins are a second (independent of USB) UART port running at 9600bps by default.
You can use u-center to modify the module's configuration, for example set the update frequency to 4Hz.