Magnetic ballast is frequency sensitive, so does not work correctly on other frequency than it is designed for. It does not mean it will necessarily damage something, but at least it will not work correctly, so e.g. underpower the lamp, flicker, ignitor interfering with the lamp when it should not and so on.

On the other hand the electronic ballasts need DC supply, so they first rectify and filter the input mains. And this work independently on the frequency, provided the filter is still able to sufficiently filter out the ripple. As all these filters are just low pass type, the only problem may arise, when the frequency become lower than designed for. So that mean a ballast designed for 50Hz operation, will work well on the same voltage at 60Hz, but another ballast designed for 50Hz may have problems at 50Hz.

So when you want to operate some lamp at 240V/60Hz, but the available ballasts are 240V/50Hz only, only the electronic ones will not have any problems, so you may use them.

cannot find any 26 watt sox-em120v 69 hz ballast

I meant to use 240V/50Hz electronic - that would work on 240V/60Hz correctly. So order an electronic ballast for this lamp from Europe and use it on 240V.

If there is no 60Hz magnetic ballast for your lamp, you have to live without magnetic. The 50Hz one simply does not work correctly and the lamp appear to not tolerating it. SO you have no option than either design and build the ballast (assembling combination of available chokes,...; but that require quite deep theoretical insight in the related math), or go electronic (the electronic at least don't care about higher mains frequency).

 

That would the only type of ready-made ballasts from Europe (where these lamps are targeted) capable to run on 60Hz.

Otherwise you have to play a bit with combining 230V fluorescent ballasts on the 240V till you get the 0.37A.

Otherwise I.m sorry, but the lamp won't work...

I just went through some fluorescent specification and have found F30T8 rated for 0.365A, so you may try F30T8, but it has to be of the full power type.
If you find some, let's post the sticker and do some measurements with an Ohm-meter, so I may help with the connection.