I have a Gerber toilet, and the toilet lists two flush modes. Do I need to install something to use that alternate flush mode? The toilet handle seems to have only one action.
It's not an alternate mode, per se. Those values are the minimum and maximum tank volumes based on float setting. [Correction: These values seem to apply to High Efficiency (HE) and Ultra-high Efficiency (UHE) bowl/valve options. Since the values are printed on the bowl, they don't tell you much about the particular tank installed. However, the stamp in your bowl does indicate which you have (1.6 gpf).]
Your toilet is no different from all those that came before in the sense that when you lift the flappy-doodle with the levery-bit all the water falls out. They're rather unintelligent devices.
To reduce flush volume, adjust the float to a lower level. There's probably an adjustment screw on it where you can move it down. This shuts off the water sooner on fill.
When I look at the Gerber website, the only models I see with both the 1.6 and 1.28 designation are bowls (which is where your stamp seems to be). Ex: https://www.gerber-us.com/product/north-point-1-28-or-1-6-gpf-elongated-top-spud-bowl/
But all the paired units appear to be either 1.6 or 1.28. So it looks like you have an assembled 1.6 gpf toilet that cannot be changed to a 1.28 gpf one just by modifying the valve.
It doesn't appear the 1.28 gpf tanks are significantly different (they don't seem to have special valves), so you may be able to just lower the water level and get most of the benefit.
Most likely your flush valve (and handle) has been replaced with one that does not have the two settings. For the dual flush units, the handles is either split in two, like a long handle for the lighter flush and a short one for the full flush, or they have an Up-Down action; lift up for one, push down for the other (this is what I have seen in Gerber dual flush toilets).. The valve itself is very different though and that's not what you have in the tank, that looks like a standard single flush valve. So the original dual flush valve either broke/wore out or the original owner didn't like it and replaced it with an off-the-shelf single flush unit from a hardware store.