According to the table on page 17 of the manual a triple-blink can mean any of:
11 Hi-limit, Igniter
12 Flame Sensor, Hi-limit
55 Main Gas Valve
51 Proportional Gas Valve
72 Abnormal Burning
If you spring for the TK-RE02 remote front panel (about an $85 item typically, sometimes less) it would display the code number associated with the error to narrow it down.
The most common issue on that list for a unit that has been in service a handful of years would be a carbon-varnish on the flame sensor. This can be a DIY remediation with a bit of dissassembly and cleaning the flame sensor with a plastic Fibertex or Skotch-brite type dish scouring pad (not sandpaper, emery paper, or steel wool, which can make the problem recur more frequently by leaving scratches where the build-up can get started.)
Takagi telephone techs are pretty patient and good at talking homeowners through diagnosis and repair. If cleaning up the flame sensor doesn't do it, give them a call as you're waiting for the remote front panel to arrive. You'll save more of your own or a pro's valuable time having one already hooked up then next time there's a glitch, and there will be. Nothing this complex goes forever without repairs, but you should be able to get at LEAST a couple of decades out of a TK Jr with a few minor repairs and maintenance, and having finer insight into the problem detected is going to be worth it- if not this time, 3-5 years down the road.