After making a video I open it in Photoshop by going to File -> Import -> Video Frames to Layers. The import preview is where you can select a portion (or whole) of the video to bring in using the sliders. Click selected range only and limit the frames to choose only a part. Hold down shift to make your selection as it plays.
To see the animation frames go to Window -> Animation
Then I deleted unwanted frames from the end and also their corresponding layers to keep things tidy (shift-click to select multiple layers at once).
To help keep file sizes down I create a static background by duplicating the last (or top) layer and going back to the first frame on the animation window. Make sure the duplicated layer is turned on. On this dup layer start to erase only the areas that have movement and you should start seeing the first frame come through.
Then I did some small tweaks to the levels and added a blue filter as adjustments layers.
To save it out as a gif go to File -> Save for Web & Devices… here you can play with the image size and colors and such to try and keep within Tumblrs size restrictions. Preview if you want then save with the default setting for gif files c: