In the upper right corner of the board is a small yellow block with a brown band on one end... That Sure looks like a tantalum capacitor or at least it looks Exactly the same as the tantalums I used in place of smd electrolytics. for coupling and bypass. Typically I would start with a 220 - 470uF elect. cap on the battery and a 100 uF elect. cap on the output of the regulator MAX683??? I really don't remember but it was an electrolytic and I just wanted 'something' there. I should stop and note that Electrolytics should be about twice as big as calculated because over any appreciable time they will always decrease in value and decrease value with temperature. MLM Ceramic capacitors were relatively new and expensive in 2008 when I retired and I used tantalums whenever I needed a stable and good quality capacitor. I would use at least one 10uF tant or possibly a 47uF tant. Cap on each design along with a 100 nF per IC. From personal experience it pays to be as conservative as possible. There is another thought too... add as many as you have reasonable room for... You don't have to populate the positions of unnecessary parts... and should the part 'somehow' be required... You've a place for it.
Finally the parts are totally invisible, inexpensive, insurance and will not limit the rise time of the regulator output voltage... unless the current limit of the IC is exceeded.
Bob