IF you do go the route to replace the burnt-out signal bulb, it would be wise to replace ALL the bulbs in the instrument panel, since you will have the expense (or your own time) for labor to disassemble the dash board to get at them. Chances are that when one bulb goes out, others are not far behind.
I do not know if there are aftermarket LED bulbs available to replace OEM incandescent-type bulbs for dashes. I would be leery about doing so if they do not have a built-in resistor, as the much more efficient LEDs tend to have a lower wattage usage that can play havoc with electrical systems if not regulated properly, as funny as it may sound. Exterior LED turn signal lights, for example, may blink on-and-off at a much faster rate because the control ballast/switch is "pre-set" to a specific resistance value in a circuit to turn-on-and-off. The built-in resistor helps to "match" that wattage. This may also explain when the turn signal lights are blinking faster on that side: the burnt- out bulb is no longer drawing electricity in that circuit and there is less resistance on that side, hence the control ballast/switch is thinking it needs to blink faster based on its pre-set resistance.
I am just guessing, since I am not an electrical technician.
I think your owner`s manual has a bulb-replacement list in the back, but that may be for easily-accessed bulbs, like those in the exterior signal lights or dome lights. Otherwise, you could use that owner`s manual list to cross-reference with aftermarket bulbs.