No none of the sleep modes currently support this, definitely not any deep sleep mode. What you will have to do is wakeup, toggle the pin then go back to sleep. The LPTMR timer just wakes the teensy, toggling is up to you.
If you just toggle a pin every second the power consumption should be pretty low, probably around the stated .250mA + whatever else you have connected, your fuel gauge should give you all that meta data? The only thing i can think of now that would consume extra power is when the toggle pin is high, it all depends what it is connected to it, you will have to do some tests. Maybe if it works like this, make your transistions LOW->HIGH->LOW?
To save power try to make any processing in between sleeps as fast as possible, so optimize your code the best you can. I'm assuming your using my library(beta)?, the "DeepSleep" routine has callback function that would be perfect for your pin toggling. The deep sleep examples will show you this.
duff
Ok, so a power consumption guesstimate of .250mA is low but not as low as I would like to go.
How about if while the battery is in the standby state I put the Teensy 3.1 into Deep Sleep only calling it wake up every 24 hours and update the battery fuel gauge data and refresh the LCD. It will continue doing this until triggered to go into active mode. So every 24 hours the Sharp Memory LCD gets it pixel data updated and then we could use a CMOS 555 Timer that consumes .144 uA @ 5v to generate a square wave at .5Hz to send the Vcom refresh pulse to the Sharp Memory LCD.
Would that allow the Teensy 3.1 to stay in a deep sleep state for all but a second every 24 hours?
If so then that would bring the stand by current down to a few hundred uA for the Teensy 3.1 in deep sleep + the memory LCD + battery fuel gauge.
Is there any reason that type of setup would not work based on the info I have provided so far? The 555 timer can generate a pulse every .5 - 1 seconds right?
Here is a video showing the low power consumption of the new CMOS 555 Timers https://www.youtube.com/watch?v=T2WXy2wW_LI
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